You can mark items as shipped in the UI, through a spreadsheet upload, via API calls, or through integrations with a number of our partners that do shipping information (that also use the API).

Yes, multiple tracking numbers are supported.  If they're for different items in the order, you should set up the different shipments with the appropriate items in each box and put the tracking numbers there.  If it's multiple tracking numbers for a single item, just send them as a comma separated list for that package and they'll be processed.