1. how can I know that I can trust a lawyer that if my idea is not yet patented it will be registered under my name ?
Seniorjudge is correct. Very, very few patents ever amount to much, and no lawyer is likely to risk his or her license to try and take your invention. Further, if your invention IS valuable, a patent without the proper inventor is not enforceable -- it would be very simple for anyone who sought to invalidate the patent to discover that the patent was not invented by the lawyer, and that the incorrect inventorship asserted was with fraudulent intent, and get the patent invalidated.
In other words, there is a lot of risk, and no upside, to the lawyer stealing and patenting your idea.
2. If I'm not a permanent resident of the US, can I still protect my idea with the US patent and trademark office ?
Yes. But if you are planning to file in other countries as well through the PCT, you will need to check if your particular status will allow you to file first in the U.S., or whether you will have to file in your own home country with the U.S. as a designated state.
If you are only planning to file in the U.S., then there is no issue with you filing in the U.S. based on your citizenship or residency.
3. What will be a fair cost of a lawyer services for search and protect a patent ?
No way to say. If the invention is a simple mechanical device, and you can find a local (or even not local) patent attorney or patent agent (either can do the work) that specializes in solo inventors, you may be looking at $3500 or thereabouts for the attorney or agent, plus whatever fees there are from the USPTO, which will vary, but should be less that $1000 for a simple patent. If you go to a large firm for help, the price for the same simple invention could double, or go even higher. A more complex case will generally be more expensive. A biotech or pharma patent may start at closer to $25,000.
There just isn't any way to tell. Because you failed to answer the question "what is your state" I assume you are outside the U.S. You can either try and find someone in your own country who is registered to practice with the USPTO (or has a working relationship with someone in the U.S. who is registered), or you can go to the USPTO website, click on patents, then "find an attorney or agent" and it will give you the list of all currently registered agents and attorneys and their contact info, and you can start contacting people. Or use Google or whatever to search for patent agents or attorneys.
