That Federal Pacific panel has to go as they are dangerous. As far as concerns about your skill, you sound like that particular kind of newbie who is well capable of learning to do it all safely and well; however my hunch is you are still thinking too much, and need to read a little more. It's OK, we all start there.
Normally, just replacing a sub panel is a straightforward thing. Change panel, reattach wires, done. However, this is only part of a project with a much larger scope. You must contemplate (i.e. ask your permitting authority) whether you have crossed the legal threshold of a remodel. If you have, everything in-scope must be done to all current codes. Even ADA!
The 2-circuit requirement for kitchen outlets is not intended to mean "1 circuit for this wall, 1 circuit for the other wall". I'd encourage some more research but if it was me, I'd interleave the outlets, every other outlet on a different circuit. Also there's nothing wrong with more than 2 outlet circuits in a kitchen, the whole point is to prevent trips when the chef is madly at work, so the chef isn't hobbled with limitations like having to put the toaster here and the George Foreman over there, and avert ugly workarounds like extension cords draped across sinks or stoves, etc.
I see you plan to go 12 AWG wire for almost everything (that's what 20A breakers mean) - that's awesome. Feel free to kick the refrigerator and smoke detector up to 12AWG also - that way you don't have to buy any 14AWG wire. I don't own any! If you have some other reason to use a 15A breaker you are welcome to use that on a circuit wired in 12AWG.
You may want to run the water heater circuit in 10/2 or even 8/2. That will allow you to easily upgrade to an electric water heater in the future. Still use a 15A or 20A breaker because the outlet is still only good for 20A. There is a trick to fitting 8+ AWG wire on a 15-20A outlet, just ask.
I would go with a much larger panel. You have either -1 or 3 circuits left, and that's too little headroom for my comfort. Getting a larger panel is dirt cheap compared to the cost of replacing perfectly good breakers with duplex breakers (I call them double-stuff) merely to shoehorn everything in. Also, larger panels in combo-packs come with more breakers and that is far-and-away the cheapest way to buy breakers. Another reason to avoid duplex breakers is if you ever need AFCI, GFCI or whatever future thing comes out - those are much more expensive in duplex breakers because of the miniaturization required. Don't think you must use a 100A panel - you can use a larger panel (200A), you just can't use a smaller one (70A).
Remember each sub-panel must have its neutral bus bar separate and isolated from its ground bar. That means removing bond straps, magic green screws, neutral bar kits, whatever the panel requires to do that. You might consider a panel with a neutral and ground bar on each side of the panel. That's a convenient feature so wires don't have to cross over the panel.
Keep in mind how your house got a dangerous Federal Pacific panel. The last guy bought cheap. Feel free to research the good-better-best that each manufacturer offers, the price differential for "best" is quite small compared to the overall cost of a remodel. You may find better selection and better prices at a real electrical supply house.
There is nothing wrong with more ground rods. Go nuts. The key is that all the grounds are connected to each other by wire - and they are not connected to neutral anywhere except one place - the main service panel.
Breakers protect wires. The wire to the sub-panel can only be protected by the breaker in the main panel, and that must be correct for the wire's type and size.
Like Ed Beal says, you don't need a master breaker in a sub-panel. The breaker in the sub-panel wouldn't protect the wire to the sub-panel. It protects the sub-panel itself, which is listed for 200A. It can also be nice if you ever get sick of paying the tenant's electric bill and have the electric company feed a separate meter to that panel - voila, the master breaker is there already!
(I'm saying "master breaker" to avoid saying "main breaker", which might be confused with "breaker in main panel".)
If you are hoping for the sub-panel breaker to trip before the main-panel breaker, that doesn't work. Breaker trip curves are complex and unpredictable.
If the 100A breaker is not listed or labeled to work in the 200A panel, then you cannot use it, end of subject. That's the law.
This is a situation where buying from a proper electrical supply house (and not a big-box home improvement store) will be very helpful. You tell them what you want, they will sell you the right thing in the first place, and stand behind the combo. On price, for the behind-the-counter stuff, I find them more than competitive with big-box. Their customers are, after all, electricians who deal in volume and drive past 3 big-box stores to buy there. (Electrical supplies do tend to wildly overprice the impulse-buy grab-candy at the front of the store, so don't go off those prices.)
This in an old (1955) GE panel that was formerly the only panel for a house with 3 phase 100A four wire service (yes, three phase). I had the service updated to 200A standard three wire and new main panel. This is now a sub panel with no separate ground. I had the breakers replaced because one of the old breakers was found to not trip on a short. Much of the circuits have now been replaced by new home runs to the new panel. The last circuit to go will be the water heater when the new plumbing is done. OK to keep this as a sub with existing SquareD breakers? 
Pix of panel
Best Answer
This panel might be OK as a subpanel, but it will be rather limited by breaker compatibility issues...
What you have here is a rather...ancient GE panel; in fact, it is ancient enough that it dates back to before the modern "double stuff" breaker type in the GE Q-line (the THQP). Instead, it calls out the thoroughly obsolete and unobtainable type TR breaker as its "double stuff" breaker type, which means that you are restricted to full-width single-pole breakers. Furthermore, it is old enough that it dates back to well before current generations of the THQL breaker design (we can tell because it calls out type TQL breakers for the single pole, with type TR tandem breakers), so you may run into issues installing new-production THQL (issue RTxxx or newer) breakers; the only way to tell I know of is to try it and see if the breakers seat down fully on the stab.
This issue is better documented in this DIYChatroom post, with the pertinent parts quoted below for posterity:
Note that even if current issue THQL breakers do not fit in your panel, you should still be able to use UL classified Eaton type CL breakers in it; however, this limits you to 50A branch circuits overall, and also means you can't get dual-function breakers, two-pole arc or ground fault breakers, or other sorts of exotica for that matter. These limitations may or may not matter specifically to you, but would weigh against retaining this panel if I were in your shoes, especially considering that it will become surplus to need in any case.
But you do need to evict the aliens if you wish to keep it, though!
If you wish to keep this old soldier of a panel in service, you will need to evict all the alien breakers, though; while Eaton BR and Square D Homeline breakers appear to fit, they are not the correct breaker types for this panel and using them can lead to trouble with the breaker-to-busbar contact system down the road. As I said before, while new THQL breakers may not fit, used or "new old stock" THQL breakers should still work, and so should Eaton CL breakers that are UL classified for GE panels.
As to how it was used in three phase service (or not used, as it turns out)
As folks may have noticed, the OP's loadcenter is nominally a single-phase, three-wire panelboard, yet it was used in a three-phase, four-wire application. How? The key in most situations, albeit not the OP's, lies in the rightmost of the panel's three wiring diagrams, where it depicts what is known as a delta breaker being applied in this panel. These oddball breakers are three-pole breakers, but with two jaws and a pigtail for the line-side connection instead of having three jaws, like a normal three pole breaker. (The closest thing in appearance to a delta breaker in today's usage is a two-pole switching neutral breaker, but those are different internally as there is no overcurrent trip in the neutral pole.)
In this setup, the two line side jaws connected to the panel busbars, which provided the A and C phases in a 120/240V, 3-phase, 4-wire, high leg delta service, while the pigtail was hooked up to the incoming B phase (high leg), allowing a three-phase load to be powered alongside normal single-phase loads, such as when a three-phase air conditioning compressor or a small amount of three-phase machinery was to be powered from the same service that supplied normal single-phase lighting and power loads.
However, delta breakers had several usage limitations, one of the main ones being that they cannot be correctly used if a two-pole main breaker or main switch is upstream of them. In particular, what would happen if you tried to use a delta breaker downstream of a two-pole main device is that the busses would stay live with the main shutoff and the delta breaker left on, as the B phase (power/high/wild leg) would backfeed the remaining phases (legs) of the service via the three-phase load.
Fortunately, the fact you had a separate main disconnect in the form of a fused switch kept this from being an issue; in fact, it does not appear that your panel ever had any delta breakers in it. Instead, the three-phase feeder to the AC disconnect was (likely improperly) tapped at the main safety switch, bypassing this panel entirely and allowing it to serve as a single-phase panel fed by the two lighting legs (A and C phases) of your high-leg delta service.
While it was possible to safely use them in main-lug subpanels fed from three-phase main panels or main shutoffs (such as if the B phase was fed to your panel first instead of bypassing it on its way to the air conditioner), in "rule of six" split-bus main panels, or in a backfed main breaker configuration using a delta breaker as the main breaker and spliced pigtails to distribute the B phase, the misapplication issues encountered in main breaker applications, along with the deprecation of the "rule of six" as applied to split-bus loadcenters, mean that delta breakers are no longer permitted to be used in panelboards atop being long-discontinued items.
Nowadays, the notion of the high leg delta itself is almost obsolete; three-phase combination lighting and power services are run at 208Y/120V, using designed-for-purpose three-phase, four-wire distribution equipment, despite the losses it entails when running resistive loads, as 208Y/120V can be subdivided (for say a multi-unit building, or multiple buildings on a single transformer bank) in a balanced fashion even when individual buildings are being fed with split phase service (120/208V 2 phase 3 wire service is commonly provided in dense areas or for individual tenant spaces/units in high-rises and other dense buildings), vs the intentional imbalance of a high leg delta configuration, and also does not introduce the equipment-damage risks that are present in a high-leg delta service due to the fact the "high leg" runs at 208V phase to ground and thus will damage 120V devices if it is accidentally used to power a single-phase circuit.