Ok my advice.

I don't know if you can root on eclair from androot but you could give it a shot it's just an app you download it you click root and that's it. Now if it doesn't work from 2.1 don't worry it should damage the phone at all and if it does trust me we can fix it then just update to frf91 (NOTE: if you go any further than frf91 (ex: frg33) you will have to root with superoneclick which is a little more complicated because you need to install drivers but not that much) so that is how I would do it.

No you can't root 2.3.4 without unlocking the bootloader but if you root then you can flash a 2.3.4 rooted ROM with no problem. And if you are on it you can always passimg back to frg33 then root with superoneclick.