Don't worry.

It depends on which state you are doing your LCA. After this, they will submit your materials to USCIS for H1B petition. Since the ISO of youe school is taking care of everything, just wait for anything they ask you to sign. So far, you don't have status problems in anywhere, just be patient.

For H1B visa, probably you need to go back to US consulate in China since all your diplomas are from there. There are cases they will accept your application by mistake, but it'll take some time to verify your diplomas. Security clearance check or not is hard to say. It depends on what did you do, and what are you going to do. It varies from weeks to months.