I have never used the double occupancy thing so can't comment on that one.

When it comes to upgrades I have been rather successful and managed to get upgrades about 80% of the time so I'm not complaining (only tried Radisson SAS and Regent hotels though).
Exactly how it works depends on the hotel, sometimes it more or less happens automatically, at other hotels you may have to ask for it and sometimes even explain that the benefit exists (especially in southern Europe where fewer EBS/EBG travel).

I usually present my EB-card at check-in and ask nicely if it is possible to get a nicer room with my card, that has proven to be the best strategy.
Just presenting the card without asking may work, but sometimes they are stressed and forget about it and at other hotels they may not even know about the benefit and will just enter the EB-number for the points.
Also, as the upgrade is at the discretion of the front desk staff it certainly helps to be nice and friendly.

When booking on the Radisson SAS webpage I once tried to enter "EBG" in the special requests/comments field and that time they had actually prepared the upgrade in advance...to a nice suite.

Some hotels have a very strict no-upgrades-for-EBGs policy but will still make an effort to get you the best room in the room category (the largest/the one with the best view etc).

If you need late check-out you may also find that they are more flexible with your check-out time, I have managed 3 pm and even 4 pm, best thing is to ask about it at check-in if it's just a short stay.