2 - Depends on what you're doing. Animations definitely run smoother and with less resources in Flash than they do in HTML/CSS.
3 - A lot of Flex's layout capabilites "just work" out of the box. You don't have to figure out the complexities of the box model and you don't have to know the intricacies of floats. You just say "I want a container that positions things horizontally and I want them to be aligned on the top of the box" and it does it.
Flex's components I have found are incredibly hard to precisely skin. Then again, so is HTML if you don't have experience in it.
And you can have SEO in Flex easily. Check it out: http://www.google.com/search?q=listen+to+free+music+online
Flash player is not so popular because it doesn't perform well. It perform great. One of the best sources to deliver video and complex interactivity such as games available.
People always attribute the low barrier to entry of flash (7you can crank out a bad website or animation quickly) to the speed and quality of the flashplayer or actionscript/mxml. Honestly, there are many more bad html/css and java sites than flash.
To make a long rant short, quality flash/flex can provide just as good (and oftentimes better) UX than anything else.
2. The flash plugin sucks on most browsers, its a slow unreactive user experience, compare a few full flash sites to their equivalent in javascript.
3. Flex's layout constructs are similiar to pretty much every widget manager around, are in no way close to the power of xhtml/css, I for one didnt find it enjoyable at all to develop for.
how long have you been doing html/css? its a pain that goes away quite quickly, if it hasnt, I would ask some more experienced developers to look over your stuff and see if anythings being done wrong.
and you might want to look at graceful degredation, if ie isnt a particularly large chunk of visitors, your exact problems are very easily solved in a way that very gracefully degrades (-moz-border-radius:, font-face:)