Hi Daniel,
We eventually decided to retain our IE setting which enforces compatibility for intranet sites (as our portal runs on this domain). This effectively meant issue 1 and 2 I mentioned went away.
Additionally, to get all ITS portal applications working correctly we had to set the iView property Launch in New Window to 'Display in separate headerless portal window (standard mode)' otherwise we had rendering problems and the application would hang.
We're aiming to transition all our web applications to a newly set up Fiori launchpad running in standards mode rather than waste effort trying to get legacy applications working on the portal in standards mode, which is a drain on resource.
Good luck.
Alan