The charging port for sure. Its not to hard to take out, just kinda tedious. Update (01/08/2016): I just reread your post and realized "dock connector" is probably the charging port. Is the Red you are talking about the "connect to itunes" symbol

low end hot glue guns opertate at 248 degrees (F) so as long asa the speaker doesnt hit that temp Id imagine it would be okay. I would test it out. Glue it and if you can operate the tablet without it being put back together, do that just to see how it holds up. Good luck!

If the screen stays black when ringing I would imagine you need a new digitizer