I don't and when I hear it, it always sounds odd..
I just love how a very simple question like this, on this site gets people talking. I very often (offen) bypass all the super serious stuff that's posted. I respect them very much, but I like to keep things lite. We don't always have to be so serious. And that's one of the many things I like about this website!
Sometimes. As with some of our other odd regional colloquialisms, pronunciation depends on usage. Example? Cuyahoga is pronounced Cuy-a-HOE-ga in reference to the county, but Cuy-a-HOG-a for the river. A lot of the time we do leave out the tees in words though. Another example, the city of Mentor is pronounced Menner.
I pronounce the "t" in "often." I also say "fewer" when referring to a smaller number of things, and "less" in reference to a smaller amount of something. I pronounce nuclear NEW-CLEE-ARE, unlike Bush II, whose won't it was to say NOOK-YOU-LAR, which is fine if you are only 5 years old or an adult hillbilly, but totally unacceptable if you are POTUS. I found it extremely funny that many of 43's Republican compatriots took to mispronouncing "nuclear" on purpose, apparently to normalize what was obviously wrong simply to show political solidarity. I see the same kind of thing happening today. Republicans normalizing and/or approving of 45's wacko behavior, aiding and abetting the covering up of his criminal acts, merely for political expediency. Unfortunately, mispronunciations and bad grammar are the least of our worries right now.