As a sole proprietor can I use my Fictitious Business Name also for my Website Domain Name?

Yes, there shouldn't be a problem with that.

RE: class action suit : I have been asked to serve as a representative plaintiff in a large class action suit involving

You should speak to the plaintiff's attorney about this.

Research time, lawsuit

Depends on the lawyer, the type of case, the complexity of the case, the type of motion being researched, etc.

How to get responding party to correct inaccuracies in discovery responses?

Yes, you should write a meet and confer letter to the other party, asking them to supplement their responses.

It depends on what your lease says about parking.

I'm being sued for personal injury. they have requested entry default letter.How do I file my response?What should I include?

You need to file an answer to the complaint before a default is entered against you. Then you can try to settle the matter.

What are the forms to vacate default judgment in Los Angeles? Are there specific forms for this?

There are no forms, you will have to draft a motion on pleading paper, following the rules of the California Code of Civil Procedure.

Changing deposition taker

No, there is nothing wrong with that. The defendant still has to answer the deposition questions.

I never got documents on a civil case on a letter letting me know that being sued by insurance company what should i do

If you haven't gotten the documents, then you haven't been served yet. Once you are served, you should file an answer.

2 Weeks Into a 2 mos stay in LA, we discovered the bed provided has bed bugs. Landlady won't take action.Legally what can we do?

You may have habitability claims against your LL, but a full consultation would be necessary to properly advise you.