2-2-2-4 is fantastic stuff and a regular recommendation from me. Heck the stuff is the price of #10 copper and carries 90A instead of 30A, what's not to like?
I have seen several prominent home off-grid power projects on Youtube fail hideously, because they got "copper-itis" and ran the #10 copper they could afford for a low voltage DC circuit that needed much larger wire. If they had run the aluminum feeder they could have afforded for the price of that #10Cu, their project would have worked!
Do you need a main breaker in the subpanel?
Well, you need a main disconnect of no more than 6 throws.
If you don't want a main breaker panel, this is a good argument in favor of getting a nice big panel that isn't HOMeline*. Because if you can avoid using tandems, you can turn 3 breakers into 1 throw using a handle-tie intended for 3-phase circuits. (Those ties don't work on tandems). So theoretical 18 circuit limit. Also most larger panels are convertible, so you can just go with a real main breaker if you exceed that.
You can put two 120V circuits on a 2-pole breaker, but then you get the undesirable effect of common trip, so one circuit overloading knocks out the other. So if you want to double-stuff a small panel, you can use dual 240V quadplexes...if you want to go that way, favor Eaton, as they make non-common-trip quads. But that trick only limits you to 12 circuits.
What do you do with ground rods?
Totally separate systems. The neutral comes from the neutral feeder to the neutral bar to the circuit neutrals.
The ground comes from the grounding rods AND the ground wire (different jobs) to the ground bar to the circuit grounds.
They are not bonded together. Two neutral-ground equipotential bonds would cause all sorts of mayhem.
Subpanel on the exterior?
no, interior is just fine. Must have standard working space kept clear at all times, so select an area that people will tend to normally keep clear, like a hallway or threshold.
Does the disconnect need to be outside? No.
What is the easiest way to read NEC online?
Trying to use NEC as a learning document is a bad, bad idea. And it says so right in Article 90.
You can sign up for an account at https://nfpa.org which gives free, crippled access (i.e. their lame UI, not a PDF) to the NEC text. however, it is behind a "signup" wall, so a bit of a privacy loss, and yet another password to keep track of.
Rules here prohibit discussing any scanned PDFs that may exist. The National Fire Protection Association is a non-profit 501(c)(3) public charity.
Really, an electrical education needs two things: first, a general book on the topic to be a well-rounded primer, i.e. to tell you which questions to ask... and then, a search engine or sources like us to deep drill into particular questions.
99% of the time you will find articles on mikeholt.com, electricallicenserenewal(?).com, ElectricianTalk, or here that will cover your question. Ugol's Law: you're not the only one.
I think it's brilliant to choose #2 aluminum. You can run that as high as 90A.
#4 aluminum is good to 65A and can be breakered at 70A since 65A breakers are not made.
I recommend breakering it for 60A. The reason is, 60A is the smallest breaker that will accept #2 wires directly.
As far as 120V vs 240V, I strongly recommend being 240V ready. Since you are direct burial you ony get one shot at this. If all you can get is 2-2-4, I would either run 2” PVC conduit so you can put in any wire you like... including fiber optic by the way. Or I would throw a 6Al or 8Cu wire in the trench for use as a ground.
Use the 2-2 as hot-neutral for now. If you go 240V later, rejumper it so the 2-2 are the hots and 4 is neutral.
* Square D also sells the industrial grade "QO" panel line. HOMeline, is their, well, home line... and as such, is not offered in 3-phase models. Therefore no 3-phase handle ties.