I first read LotR about twenty years before the movies, so for a long time my inner images of the characters were more influenced by illustrations (most notably those in David Day's notorious
Tolkien Bestiary, which, although freighted with non-canonical interpretations, had lots of beautiful artwork) and the Bakshi cartoon, but some characters remained rather hazy for me, because none of the visual representations I came across quite hit the nail on the head.
In the meantime, I've sort of adopted some of the movie characters, because they more or less fit what was in my head anyway and added detail to my preexisting image; others not so much.
The hobbits : have always been the least well-defined in my imagination, I'm afraid. Sean Astin's Sam works very well for me, Merry and Pippin sort offish, and Frodolijah not at all. Frodo should look several years older (and wiser and more elf-friendish, if you get my meaning), Pippin the reverse (he was the youngest of the four, not even of age yet - a teenager, if he was a Man).
Gandalf : McKellen was perfect as Gandalf the Grey, not quite so perfect as the White (but that's more a makeup issue - are we to suppose that his hair & beard were singed off in the fight with the Balrog, or why were they trimmed?).
Aragorn : now he may be the one I saw most clearly with my inner eye before the movies, and Viggo never came close for me. I've always pictured him as a sort of Leatherstocking figure, at least in his guise as Strider the Ranger; to be more specific, my Aragorn is Hellmut Lange, the actor who played Natty Bumppo in a late 60s German TV adaptation of Cooper's Tales which I saw as a child. Some pics:
Imagine him with longer hair, add a cloak and replace rifle with Andúril - that's my Strider!
On the Anduin:
http://www.bamby.de/1969/Leder-1a.jpg
With Hasufel:
http://www.tv-nostalgie.de/Bilder%20Lederstrumpf/2h.JPG
Bakshi's Aragorn wasn't too bad either (but give the poor guy some pants!)
Boromir : I like what Sean Bean did with the role, but both Boro- and Faramir should be dark haired, and Fara could do with a little more edge.
Legolas : should have darker hair (could be a darker blonde, auburn or any shade of brown, I don't care which), lose the fancy hairdo and cut it a little shorter (imagine him moving in the thickets of Mirkwood with those tresses - ouch!).
Gimli : John Rhys-Davies minus the comic relief would do nicely, but he should wear a hood instead of helmet prior to Helm's Deep.
Elrond : I found Bakshi's Elrond lacking in elvishness, but he's still better than "You've been leading two lives, Mr Aragorn...".
Galadriel : Cate Blanchett did a very nice job, but I imagine the Lady with a slightly more, er... motherly figure, and her hair a more reddish-like blonde, to contrast better with Celeborn's silver.
Saruman : see Gandalf above, only without reservations.
Théoden : should look a little older than Bernard Hill; long white hair & beard.
Éomer &
Éowyn : more or less as in the movies; Éowyn maybe a litte sterner and cooler.
Denethor : movie-Denethor was a disgrace, both visually and as a character. My Steward is a much more ascetic figure ("...lest with age the body should grow soft and timid"!): lean and haughty, with an aquiline nose, whitening hair and a neatly trimmed greying beard. (No idea where the latter comes from - it's not essential, but that's how I picture him. And no, he doesn't munch cocktail tomatoes, thank you very much.)
That's more or less my somewhat unsystematic response to questions 1.-4. As for 5.: yes, I've tried to draw some of the characters the way I see them, but being the perfectionist I am, I'm not quite satisfied with the results.