A: There's no real way to know how long this action would take, because we're talking about government. however, you should assume now that that your tax refund will be taken by the state. If nothing else, pay the first $250.00 because that might delay things a bit. Figure out an alternative to getting your LL the rent.
A: The third party person who pays for the litigant's attorney has no say in how the case progresses, because the payor is not the client. Neither clients nor payors dictate anything; the case progresses according to the law as applied to the facts of the case. If you think that you are going to tell the attorney how you want things done, or what to file because you are paying the fees, you should disabuse yourself of that notion. I daresay the person for whom you are paying the fees would find him or herself without an attorney fairly quickly.