Yes you are eligible to file with no problem.

Just leave within 2 weeks if the letter does not give a time.

Should my fiance and I get married and file for the greencard, or have him return to Italy and apply for a fiance visa?

Go ahead and get married. No problem. And congratulations! I've had many clients do this and I prepared all the paperwork. It turned out fine.

10-point executive action on immigration

We have no idea whether or not these things will take place. It's useless to analyze.

An NOID gives you an opportunity to respond to the reasons USCIS wants to deny you. You should get some help on that.

Dear Sir /Madam Can I apply for tps if i already applied for asylum-month ago- and i am still waiting for the decision .

TPS does not affect an application for asylum or any other immigration benefit. Go ahead and apply.

Can a US Citizen file Green Card petition for in-law?

The answer is no way in this lifetime.

Concurrent I-130 and I-1485 for my mother.

That fedex receipt you have is enough. Hopefully you have a copy of what you sent.

I130 and i131 under Deferred Action combined ?

Yes, she can apply for a travel document. However, they are very difficult to get when you are DACA. If it's an emergency, it's easier because it...

Obtaining a visa in Germany

You need to ask a German expert, not US lawyers.