Will try to answer them all based on the is series lol
1. Not really the only major problems are with the 220d but I suspect that will be out of your budget
2. As above the D's have problems but for a 7k budget you wont find one, if you can stay away it'l be a dog
3. The sportcrosses were rearer and thus finding scrapped ones for parts will be harder, dealers still fully support them though so serviceable parts shouldnt be an issue
4. Depending on the age the earlier IS cd players had jamming issues, other than that though most the range are pretty bomb proof nothing to worry about that arnt wear and tear issues ball joints, suspension clunking, that sort of thing
5. Insurance will of cause depend on what you go for but like for like the is200's are ceaper to insure than 320 bmws c200 mercs and a4 audis im paying about 500 a year and 26 with a prang my dads paying about 300 at 50+ and clean licence
6. The se and sports came with the premium audio pack which was fully amped with a 6 disk in dash changer unfortunately theres no ipod/phone support as standard athough for less than 150 a grom kit can be acquired which will give you full support
7. Theres lexus dealer in nottingham on the way into town just past notts uni on derby road shares with the toyota dealer, not sure about derby but in your address bar type lexus.co.uk/dealer ie lexus.co.uk/derby for details of dealers in your area
For your 7k you should be able to shop around and get a nice late se/sport is200 without any problems the later ones came with fill leather rather than half suede, check for a cambelt service its supposed to be 6 years / 60k so all 1st gen is's should have had at least one done now if not expect a 4 figure bill including service at a dealer poole quoted me 1100 quid for a full 60k service and mot last year, The sportscross will be harder to get hold of and can fetch more of a premium due to that and if you dont need and estate I really wouldnt bother the boot of the 200 easily fits 2 sets of golf clubs.