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.
That is an old "rule of six" panel, which while grandfathered, is illegal under its grandfathering becuse it has 7 main breakers. Going to five is a good plan.
It is a classic "CH" panel which is a very good industrial grade panel, except that the 3/4" breaker width make non-ordinary breakers very expensive (a trait it shares with Square D QO). That makes it perfect for what you plan.
On your subpanel which would be near this panel, I would get a panel with a main breaker, with an eye toward (at some point in the future) cutting it over to be the main panel. In a subpanel, the "main breaker" is nothing more than an on/off switch, it is OK for it to be larger than the feeding breaker.
I would also get a rather large panel, at the very least 42 space and even 60 or 84 if practicable: because panel spaces are dirt cheap and often even come with free breakers, whereas running out of space is painfully expensive.
I would aim for an industrial grade panel of good repute (one available in 3-phase variants, not Homeline, BR, or second tier brands) and avoid the expensive 3/4" breakers (not CH or QO).
Over time, as you find it convenient, i'd migrate all your 1-pole and smaller 2-pole circuits over to the new panel.
For your garage panel anything would do, but I'd go for the same type as your indoor panel, so you can use some of those bonus breakers. Again it's false economy to scrimp on spaces, I'd go 20-30 at least.
Also, since garage spaces need to be on GFCI, consider getting a subpanel which has a "main breaker" which is GFCI, that way all the breakers in that panel would be protected (at the cost of potential nuisance trips, a big deal if you keep a freezer in the garage).
Ed Beal raises some very good concerns about overall capacity. One problem with these "rule of six" panels is there is literally no main breaker to stop you from drawing more than 150A. So it pays to be conservative.
It's a difficult situation because you have two big loads that operate sporadically - the EV charger and the range. And the A/C as a wildcard.
One thing I might suggest, is feed the garage subpanel from the new primary subpanel. And then move everything but the range over to the new subpanel. At that point the only things still in the CH panel would be a 60A range breaker and a 100A subpanel breaker. Even at max, those two could not overload the 150A service (by enough to matter). This would force your entire house (from A/C to EV charger) to share 100A, but would remove the possibility of an overload. This would also save you the $85 you'll spend on a second 100A CH breaker.
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What kind of closet will this be? Can't put a panel in a clothing closet.
A bathroom needs a 20A because a hair dryer is 13A all by itself nevermind the curling iron or hair straightener often set out to warm up while it's in use. Also whatever else, and lights, fan, heatlamp if that's on the circuit too.
I get your idea that it's YOUR house and YOU can cheap out on the electrical system and use your smarts not to overload it. However a) don't overestimate your sense of load size. b) I certainly hope for your resale value that you are not the last human who uses this house. And c) I fail to see the value of cheaping out on electrical. Given the astonishingly low cost of the parts, you should be optimizing for performance not economy. Case in point:
The ampacity of the subpanel
First, separate the supply breaker from the subpanel proper. You can have a 30A breaker in the main feed a 225A panel (the 30A certainly won't melt the 225A panel!) The reverse is not true, obviously. You would go with a higher amp subpanel mainly so you have extra breaker spaces for future expansion, because running out of spaces is a nightmare that is so easily averted right now, when you buy the subpanel, and extra spaces are cheap. So in your case I'd go for a 30 space for instance. Finishing with 60% of your spaces unused is a good place to be. It's so easy and cheap to just add circuits if you have the panel space, so things like under-sink water heaters, electric car, welder, become easy decisions.
Beware of double-stuff breakers. Many panels advertise "24-circuit (12-space)" - the 24 circuits relies on double-stuff breakers, which are more expensive. Those are bad news because increasingly you are required to use exotic breakers like GFCI, AFCI, 2-pole and the like, and those cannot be had in double-stuff. So you are stuck with the lesser capacity e.g. 12 circuits. It's cheaper to get the number of spaces you want, so you can use the simplest breakers allowed.
Which panel? The breakers must match the panel. Eaton CH panel, Eaton CH breakers. Most manufacturers make several incompatible lines (CH/BR, Homeline/QO, etc.) The ruling factor is the cost of exotic breakers such as GFCI, AFCI, 2-pole GFCI and the like. So you can cross off several models. Those exotics are being forced down our throat, so get used to them. I am also not a fan of tenant-grade cheapies (Homeline, BR). Siemens has a lot of promise: quality panel with sanely priced exotics.
The panel should be fed with a 2-pole breaker in the main panel, unless you are doing something intentionally weird, but then why would you use /3 feeder? You should know this, by the way.
I'm a little concerned with a knowledge gap here, and encourage you to hit a library for a book on wiring houses, and read it cover to cover. You don't want a knowledge gap. You especially don't want one after the drywall is up but before inspection. If your skill is lacking, do the works in EMT conduit so it's easy to fix later!
The circuits
Now, you say you want to run /3 cable. Either you don't know what you're saying, or you intend to double the circuit so you get 2 circuits out of each cable (a multi-wire branch circuit). That's awesome. (MWBCs not unfamiliarity).
I was a little worried that you were underpowering things like the bathroom and kitchen, but if you intend to supply them with a /3 and MWBC, that means double the circuits, and the cook will thank you. However MWBCs absolutely require a 2-pole breaker, which means you will need 2 breaker spaces for each one. Like I say, you go through spaces faster than you expect!
Honestly MWBCs are falling out of style because so many circuits require GFCI or AFCI. And that requires either the uber-exotic 2-pole GFCI/AFCI breakers, or correct branching at the destination and then GFCI or AFCI deadfaces or receptacles. And the savings is pretty small compared to running 2 separate /2 cable runs and avoiding MWBCs altogether.
The bathroom(s) require following one of two strategies:
Each bathroom gets a dedicated 20A circuit for ONLY loads in that bathroom, including wired loads like lights, fan, etc. I am not a fan of this one, because BOOM you are now in pitch black, holding a red hot hair straightener 1/4 inch from your ear, and can't even set it down because you can't see to not set it in the sink full of water. (however if the hardwired loads together exceed 50% of circuit capacity, looking at you fan-heater, that circuit cannot serve any receptacles at all, and this method doesn't work.)
A dedicated 20A circuit serves only receptacle loads in any number of bathrooms. The hardwired loads are served potentially from other circuits that serve other rooms.
There is one circuit that you really will want to be 100% dedicated, and that is the refrigerator. Code requires a GFCI since it's in the kitchen, even though that's not really the use-case GFCIs were intended for. And you really don't want any other appliance tripping the fridge and ruining your food. For this reason GFCIs on fridges are a terrible idea. I say install a dedicated circuit with a single (not the usual duplex) receptacle, so only the fridge can possibly be plugged in. Use a GFCI breaker, and I would certainly never tell you to switch it to a plain breaker 5 minutes after the inspector walks out the door.