I have a PSP Slim.. Its awesome
1. In terms of music quality, It beats My ZEN and My fiend's Zune. I tested with my Sony MDR-EX51 ear bud. It sounds so perfect. You don't need a mp3 player anymore. BUT it does not support multi-level folder. So if you want to put MP3 in it, the folder structure must be: \MUSIC\<artist directory>\<all mp3s files> or \MUSIC\<All mp3 files>. 1st structure is better if you want to put 100s of mp3s. its easy to browse artist wise.
2. Video.. Ah.. Whats a Screen... Best screen I have seen on a portable device.
3. Now thats a problem. Sony as usual, do not want people to mess around with their devices. BUT there is a way around. You have to install custom firmware. Thats a expensive process unless you know someone who has a PSP with custom firmware. I had to invest $26 to buy a spare PSP batery. Yes! you need a extra battery to install custom firmware. That will allow you to do all those stuffs that Sony don't want you to do.

further details I guess you can google
4. I don't know the price in India. I've got a PSP slim Daxter edition for $190 when it was released...
5. Go Slim.. its slimmer, lighter and it has 32 MB more RAM. And ofcourse its new model.
6. It does not come with any internal memory. So, you have to buy a memory stick. Do NOT buy any chinees made memory card. Make sure it supports MagicGate. I remommend a 4 GB. Sandisk Ultra II. I got it for around $40 from ebay. Be really careful when you buy memory card from ebay or any other online stores. You really need 4GB atleast. 8 GB are really expensive.
Hope that helps