4. is it a good idea to get a psp at all? i mean, it's a rather dated piece of hardware. will there be a psp2 or comparable in the near (1, 2 years) future?
Well it's not dated as far as handhelds go.. it's the best there currently is. :p
I do expect Sony to come with a successor someday, but probably not anytime soon. Perhaps in a year or two, three, perhaps even later when the PS4 comes out.
i don't want to use it primarily for playing games, but to experiment with it. are hardware mods necessary to execute own code?
No hardware mods, but you do have to install a different OS version. Something that theoretically could screw up your PSP. If you have the unofficial homebrew capable OS installed, you won't be able to play the games you've bought though.
So either you'll be switching between OS versions a lot, or you could buy two PSPs. One for homebrew and one for official games.
Trying out your own stuff on the PSP is cool though, but for me not worth screwing around with the OS so much,
3. does there exist a small keyboard as extension, in case i want to surf with the psp?
Not that I know off, but don't worry.. you can type in a sort of pseudo-sms style, that works incredibly fast actually.
do there exist any umd recorders, or is it all memorystick-based?
I have no doubt that you could burn a UMD disc, as it's similar to a mini-disc / mini-dvd kind of format... but I do not think such burners are available for the general public.
Not really an issue though, as the memory stick is what you'd want to use anyways. Things on the memory stick usually run a lot faster.
Cheers