What should be the correct application type selection in this scenario ?

The better answer is the second one.

Can i travel inside the US with my foreign passport and the i-797?

Yes you can travel but you are risking a lot. Just applying for a U-visa does not protect you from being arrested and deported. Having a...

Please provide your inputs on my questions below urgently.

My input is that you should discuss the matter with your husband's attorney.

If I leave the country while my COS to F1 is pending, will it negatively affect my immigration history?

You can certainly leave the country but the change of status application could be denied. Leaving the United States now will not have a negative...

Yes the I-485 can be transferred. You can call the ombudsman for USCIS if you have concerns or schedule an InfoPass appointment.

I have daca what can I do so I can stay here legally and continue to work after my daca runs out ?

Take the opportunity to apply for and use advance parole. Then get married to a USC or LPR. After the marriage apply for residency. Then you will...

H1B (3 Years) to F1 to OPT to H1B (Transfer or New Application)

1. Yes you can use the remaining three years. 2. You do not have to wait until April. 3. Your employer should file the application for you.

What would be their next step?

The process to remove the conditions can take more than one year. This has become normal.

The change you made makes no difference. You will also need to pay the visa fee.

Updating my previous question - Should I make change to the petitioner name?

Your change make no difference as it is the proper name of the company.