2. H1B is allowed to attend school, however you needs to maintain status at the same time.
3. GC is for future job. Theoritically as long as your employer continues to sponshor your, your GC is fine. In this case, both you and employer has to commit to CIS that you will take the proposed position when your GC is approved. However in case a RFE, if you are not already in the position but in the school, it is hard to convince CIS that you will be back to the position at the time they approve you.