If a person has an immigration code of p22, how can they change it if they are over 30, do they need to change it?

I agree. No possibility of changing admission classification unless a mistake.

For how long parent can stay in US when B2 extension is pending? Can they stay more than 1 year while the case is still pending?

If want to remain over and above the 6 months of EOS already asked for then need to file another EOS in a timely fashion.

You are now cap-subject again until further notice for the reasons listed by attorney Behar.

Is the form I-944 household size the same as the household size of form I-864?

The household is 3 in all forms to be submitted.

Visa was cancelled/revoked for reasons unknown here.Can reapply.

I see no problem in your receiving such payments while on F-1.

Likely possible talk to your DSO and obtain his/her cooperation.

Can I have a layover in another city while my USCIS application is pending?

You will face no issues for this layover.

Even in state colleges that "don't care about immigration status" that could go against your F-1 visa terms.

Can I travel ?

Can travel with proper return admission documents.