The TB test and 2nd attestation need to be done by the beneficiaries in the first 90 days. I would apply for benefits first (SNAP & Health insurance). For most then they will want work authorization.
For Driver's license the state have differences but mostly similar. In Maine they request SSN, but in the fine print you can explain why you don't have one. (We did explained that not yet, waiting on USCIS/SSA to process.)
Yes. On the I-912 it is noted that it is for the I-765. And they are sent together. I don't think you should send check with I-912, we did not. I would recommend applying for benefits (SNAP and health insurance) first. If you can show the beneficiary is approved for SNAP, etc put it on the I-912. This will almost automatically approve the I-912.
-Kineo