Have you considered a remote for the house end of the garage hookup? I'm thinking a z-wave controllable light switch or something in the garage, and a remote control in the house. That way you can ignore the 12/3 romex and weird wiring (of that part of the circuit) and get on with your day.
I'm unclear whether it's allowed by code (especially with the colors you have), but with 3 wires, you've got enough for a single 30 amp circuit - ground, neutral and hot. Is that enough for the garage? That would at least be safe.
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.
Best Answer
The flexible armored wire you are seeing is often referred to as AC or BX cable. (BX was a brand name like Romex is for NM) Bx was used extensively prior to 1960ish and is still used today. There are no current code requirements that require this kind of cable in residential construction and it has almost all but been replaced with NM. As you have probably already figured out, BX uses different box connectors, and many of the device boxes you have in place were probably made to terminate BX cable.
Although it is perfectly legal to use, and actually quite safe, it is rarely used because of it's higher cost and relative difficulty to install and terminate. The only caution I would emphasize is the ground conductor in older BX. it was very common not to use a separate ground conductor when using BX, and often when there was a separate ground wire, it was a smaller AWG that the black/white/red current carrying conductors. this was never a problem if the BX armor was properly attached to the metal junction boxes and again properly connected at the panel, thus making a substantial grounding path.
As far as the bonus question. BX is heavy and probably brings a good price at the metal recycling brokers. A couple of years ago when junk metal was really hot, a good load would have been worth hundreds of dollars. It was a popular find for junk dealers and the target of theft.