(1) How can a contract attorney provide legal research & writing services to lawyers in other states? Doesn't that run afoul of the Rules of Professional Conduct prohibiting the unauthorized practice of law?
No. The Rules of Professional Conduct in all states contemplate that an out-of-state attorney can provide legal services to a lawyer in that jurisdiction on a temporary basis as long as the contract lawyer appears with or acts under the supervision of local counsel.
By definition, you (the hiring attorney) will be supervising my work. You will be actively participating in and sharing responsibility for the representation of the client, thereby safeguarding the interests of the client, the public, and the courts of your state. I will only be performing the background "grunt work" of reading, researching and cite-checking relevant case law to ensure that your clients have the strongest legal arguments on their side.
Similarly, pro hac vice admission is not required because I will not be conducting any activities in another jurisdiction without the direct supervision of an attorney licensed in that jurisdiction.
For attorneys who bill their clients by the hour, you may be able to bill the client in turn for my legal services, and thus recoup all of your costs.
Because there is no uniformity among the various states' Rules of Professional Conduct as to how fees may be divided among attorneys not admitted to practice in the same state, I advise avoiding fee division altogether and using instead the simplest method of billing:
You should obtain your client's informed, written consent to both (1) the working arrangement and (2) the fee for legal services being billed to the client. This is easily accomplished by using a straightforward disclosure form like the one that can be found here.