1) Yes
2) How old is this bunny, has your friend told you if he/she has had veggies before? And what kind of lettuce? Best thing to do is SLOWLY introduce veggies, one day he can have 1 small piece, next day 2 small pieces, then maybe a break, day 4, 3 small peices, and so on and so on. What are you giving him as treats? Best thing to use as treats are vegetables or herbs.
3) Yes but make sure he/she is not chewing and eating it.
4) Yes they will, and most LOVE them, but a cardboard box the same size is just as good as long at the top can support the weight of them sitting on it.
5) Try and litter train him, odd are he will pick a corner to pee in, get a plastic litter corner or box from the pet store and take the peed on bedding and place it in there and put it back in the same corner. He will (should) keep going back to pee in that corner, you need to help him along with the poops by cleaning those up and placing them in the litter corner, eventually they will catch on about the poops. Once hes litter trained you only need to change the litter corner daily, the rest of the cage can be left and changed as it gets dirty depending on what you use as a bedding (towels, plain floor, shavings, etc). For now until then, clean daily.
There are some great documents in the library on the forum that will tell you alot about what youre asking and need to know
here is some info on bunny safe fruits and veggies
http://rabbitsonline.net/view_topic.php?id=54630&forum_id=17
http://rabbitsonline.net/view_topic.php?id=13618&forum_id=17
Remember Leafy green veggies! Try not to feed fruit at all until the bunny is older as leasy and in moderation!
Litter Training
http://rabbitsonline.net/view_topic.php?id=12213&forum_id=17