If I am applying for I130

Both of you.

Can an illegal immigrant purchase a home and put in under his/her name.

If she is not seeking any loan, then it may be possible. Any bank involving will require compliance with the REAL ID Act and could have problems.

Do i need to file my H4 visa while my H1B is under processing?

You file for your H4, not your wife. If you filed to change to H1b, and you want to change to H1b, and that application is pending, you should not...

Would the I-130 Approval notice get an automatic update from USCIS or should I write to them or go to local USCIS asking that?

If she is in the US just file for adjustment. If not, notify the National Visa Center.

Are Vawa cases still being processed at Vermont?

13.7 months on average.

Can marry us citizen with outstanding deportation order?

If he entered legally, and did not violate any order granting voluntary departure, and was not found to have submitted a fraudulent asylum...

In most states, if the marriage is valid where it took place it will be recognized. So get an attorney to do the requisite research on your state...

Interested in green card. Can I apply for it or take a waiver first?

You need a waiver approved before you file.

My husband had an interview overseas and he was given a 221G denial. What shall I do to make sure my husband gets a visa soon?

File a corrected I-864 with an explanation and follow up with the embassy by internet.

H1-b visa transfer

Request an expedite, since the visa could be denied and any employment could turn out to be unauthorized.