If I file bankruptcy for my Inc company, can I still continue to work with the same?

There is no way to answer, since we do not even know whether the company would file Chapter 7 or 11. That is the first step. If it is Ch. 7, the company closes. If a Chapter 11, employees can often remain employed. Whether Chapter 11 would really have a chance, or allow you to keep trailers and other equipment is a whole other question. If the company can't keep paying its bills on a cash basis, and work out deals with secured creditors and fuel supplier, there is little chance of it going anywhere. In addition, a good Chapter 11 lawyer will be several thousand in fees for a Ch. 11 (plus $1039 filing fee).

It depends on what chapter of bankruptcy is filed; if it's a Chapter 7 then the answer would be no.

Depends on your trustee, the type of bankruptcy you file, and who owns the equipment. Corporate assets are not exempt and must be turned over. You should hire an attorney to help you.

yes, you may be able to work for the company during and after the bankruptcy. The bankruptcy court may need to approve this employment

You need to speak with a bankruptcy lawyer near you to see what your options are. The kind of bankruptcy you file (which chapter) will determine the answer to your question. In chapter 11, you will probably be able to do so. In chapter 7, probably not.

which kind of bankruptcy ?

It will depend on which chapter you file. If the company files a Ch 7, no. There is not a discharge granted, but the company cannot continue to do business. If the company files a Ch 11, yes. That is one of the purposes of a Ch 11, to help companies keep functioning while they get over some financial difficulties.