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.)
Best Answer
1) can't happen without the power company's consent, and the meter pan and service drop up to the weatherhead must also be rated for 200A. If those aren't true, you can't do #1.
2) is out of the question. The old setup was legal because it was so small it qualified for the Rule of Six (six throws to turn off everything). And the maximum theoretical load, all circuits at redline, was 125A on one pole and 150A on the other. That is such a modest oversubscription that since the Rule of Six was allowed, a main breaker wasn't really needed. However, different deal on a modern 30-42 space panel with 200-400A of breakers provisioned on each pole. Besides, the Rule of Six is now outlawed! You must have a main breaker today.
That leaves #3, and I recommend switching panel brands to one where a 100A main breaker is readily available. Unless you plan to have a generator; in that case stay with Siemens but swap it out to a main-lug panel (why pay for the main breaker) and fit their generator interlock.
You can also backfeed this panel and ignore the main breaker, but I do not like panels where the main shutoff is not obvious. In an emergency, people don't rise to the occasion, they sink to the level of their training. In other words people get stupid in key moments. Someone frantically working in the dark is gonna grab the big handle and go THWOP. And he will expect the power to be off at that point. So if that does nothing and you have to shut off one of the regular breakers, well, that's just confusing...