After search process of a patent, can I use that search info and have a different attorney write the patent if price is better?

yes, but you might get what you pay for. It is possible that the attorney that completed the search has a better understanding of the innovative aspects of your disclosure and is factoring this knowledge into the price quote. It may be worth asking the two attorneys the basis for the price quotes, and specifically why one is more than the other, to make sure that you are comparing apples to apples.

Given that your patent application will likely be pending anywhere from 2 to 5 years it important to find an attorney that you can see yourself working with into the future. It is probably more important that you have a trusting attorney-client relationship with respectful and open lines of communication even if these somewhat intangible aspects cost more.

Yes. Assuming you pay for it, you own the results of the patent search.

Yes. This is America and everyone has a 6th Amendment right to counsel. I would choose an attorney that has experince if filing patents in the same technical art as your invention. I good place to start might be to review the patents that are considered to prior art to your invention. Then, go to the Patent Office and look up the patents. The Patent Office lists the attorney and firm that wrote the patent. I would then select several attorneys contact them and find out if there is a conflict of intrest, this is called a conflict check. Once you have a couple of attorneys that can work for you, then you can do some research on them here a Avvo, and Martindale-Hubble.

I hope this this helps.

Paul