How can I switch to National Guard from Active Duty and reclassify?

While there are a few exceptions out there, you do need to understand that by-and-large, the military, even the state military, does not allow family members to serve together in the same unit.
This is due to the chance of favoritism in the wrong place (ie, when you are deployed). They will allow you to serve in the same state, but it is very possible and even more likely than not, to send you both to separate units.

However, this being said, the only way that you can transfer to ARNG, you must separate from the Army. The only way to voluntarily do this is via a Chapter 6 (Voluntary Separation), which is entirely up to your Commander's discretion. Most Commanders will not approve the request unless it is due to Family Hardship (special childcare or medical needs that require your presence, and you have another job on the outside that pays better).

My advice to you; you've only been in for a minute. Finish your contract. Because right now, unless you do so as a reenlistment incentive, you will not be able to reclass. The in/out calls do not allow for it at your level. Keep your nose down and do the duty that you volunteered to do before you start trying to play the field. Trust me, you have no clue how many way even a simple request to (even by perception) turn back on your contract can screw you in the long run.

To reclass, you can check our options when your reenlistment window opens. As for changing to the guard, you have to wait until your enlistment is up. You will see a career counselor as part of the process. They can enlist you in the guard at that time.
They’re not going to let you out of your contract to transfer to the guard. Especially at this early in your 1st enlistment.
You won’t have to go OSUT to transition to 11B. You’ve already completed BCT. You’ll just have to do the AIT portion. The chances of you and your brother doing that training together are somewhere right around zero.
Drill pay is basically 1 day of active duty pay per MUTA. Each drill day is 2 MUTAs. That’s 2 days of pay per drill day. The 2 weeks of AT pay is straight 2 weeks of active duty pay.

Can’t talk to reserves/NG until you have 6 months left in your contract. There’s no way you can switch over mid contract

Wait till your contract is done get with your retention NCO and request to reclass to an 11B and airborne in your new contract. Don’t go in the National Guard whatever you do just don’t.

Reclassinbg to 11B should not be a problem as we need them more then ever but 11B P for Airborne would open a lot of doors for both of you....

Well you cannot switch from active to Guard while you are still under contract with the regular army. At the end of you enlistment you can join the National Guard. There are in service recruiters so you can donit at your duty station, however I recommend that you go home and do it with a National Guard Recruiter in your hometown. That way you can check out the units near you and the Recruiter will know which one is a better choice. No chance that the in service Recruiter will have that knowledge. As for One Unit Station Training the answer is no you will not be going with your brother. They have reserve component reclassification school which is what you will attend.

Can't cancel your contract, you signed it. Finish it then try for something else. They'd gladly take you for guard. Infantry isn't much better.

Drill pay you get one days pay at your rank and TIS for every Unit Training Assembly (UTA). A UTA is a Minimum of four hours and a typical weekend Drill is a MUTA 4, or 8 hours training time as a minimum per day. So for a MUTA 4, you get 4 days pay. AT's and full schools or the title 32 duty are paid just like active.

Do you have plans as to what you're going to do to make money the other 28 days of the month that you and your brother aren't working in the Guard?