1. You could ask the office that handles immigration matters if they'd be okay with weekly status updates.

2. I'd maybe send them an email right now informing your future manager about your current situation and ask if, in light of that, their original recommendation that no prep work is needed still stands. Once your immigration papers are successfully processed maybe you could send your future manager an email saying something to the effect of "_My immigration paperwork is now complete! In light of that I'm wondering what my start date is?_" or something.

Constant communication is not needed and might prejudice your future manager against you (ie. he might see you as needy or something)