What happens to my priority date of May 2014 after I switch to a new employer who won't start PERM till 6 months after I join?

There is a very good likelihood you will need to start over. Without more, nobody will be able to give you any advice.

If your marriage is real, it is real. You need to work with an attorney.

For EB5, Does the investment amount have to come from outside of US.

You are in need of an EB5 specialist's advice. Do not waste your time on internet forums.

How is an H1B worker's status effected while undergoing basic training under the MAVNI program?

You have to speak with your employer and your attorney.

Renew a 2 years greencard

I doubt that the local office will be able to help you. You need to have proof of filing for them to give you a stamp.

Can I or Should I file GC for my sister who is overstaying for more than 1 year

First it is is going to take more than 10 years. Second, she still will not be able to adjust without a waiver and leaving the country.

How can i petition a relative in the Philippines?

You need to submit I 130 form. You can check our processing times on USCIS website. Also, you need to check out the visa bulletin to see how fast...

Will it be valid to use my two published articles to apply for EB2-NIW visa?

You need to consult with an attorney. There are many requirements that should be met to estimate your chances.

What should we do now? Is this letter going to affect the proceedings?

She needs to contact Immigration as soon as possible to let them know that she is willing to continue the process.

Does business like buying four apartments and rent them apply for L1 visa?

I do not think so without knowing more.