CAN HE LEGALLY DO IT?

Yes, this is fairly common in fact.

Eviction of Trespassers

Yes, you have the right to evict them.

The timeshare contract you signed would govern, so it would have to be reviewed to properly advise you. Not paying shouldn't affect your credit...

Can a sole proprietor using a dba similar to its corporate entity name and without legally registering the dba, sue in court?

No, you can only sue as an individual "doing business as...", or as a registered business entity "doing business as..."

How will the filing of a 2nd amended complaint affect a federal civil case if a motion related to lack of standing is pending?

You would need leave of court to file a 2nd amended complaint.

Renting in NYC but working in CA

Yes, either should be fine.

Does my mother need to go to court?

If your boss keeps bothering your mom, she can try and run the issue by HR.

About to close escrow. We made an agreement with broker for a 1% concession back to buyer. Now he is not willing to.

It appears you are entitled to the concession, but everything would have to be reviewed to properly advise you. You can then have an attorney...

CLOSED OVERDRAWN BANK ACCOUNT

Dispute the entry with the credit reporting bureaus.

In demand for production of documents can I ask for bank documents of his spouse?

Yes, you can ask, but you may get a privacy objection.