Can a TPS file for H1b ?

There are several questions here. It may be beneficial to apply for the second EAD under TPS. You can apply for H1-B. It would be best to have a...

It is okay. But as my colleague has suggested you should always travel with your passport with your full name,

Cancellation of removal

The main thing for you to do is remain in touch with your attorney.

Marrying a US Resident what is the process and what is the waiting time?

There is a long waiting period for spouses of green card holders to be eligible for a green card. Generally the spouse has to maintain lawful...

Form G-28 and naturalization

As long as your attorney has filed the G-28, then he should also receive the notices.

Hi, can we travel out of US while I-94 is under extension process?

You should wait for the extension to be approved before you travel.

I overstayed my visa, I am married to LPR, who is eligible for citizenship soon. If he files the I-130 form before naturalizing

Probably not. It would be best to wait to file the I-130 after he becomes a US citizen.

Can I get a visiting or job visa for my husband , after applying for him?

Yes if your husband qualifies, he may apply for a H-1 or L-1 visa. Both of these visas are working visas which allow your husband to be in the US...

Naturalization and moving ?

You should submit an AR-11 to the appropriate USCIS office with your current address.

My Citizenship application got denied, if I appeal how long does it take for my second interview to take place?

I agree with my colleague. Generally it is better to file a new application rather than wait for a date for your appeal.