How to film your DS screen

Your first question was asked and answered here,
your second one here,
your third is not really appropriate, it's too localized and also subjective, there's not a real answer I can give you,
and your fourth is answered here.

Please read those, you can comment on them if you still have any questions about those topics.

Technically speaking, that'd be the Dreamseeker. Obtained after defeating the Dream Devourer, it boasts an attack power of 240 (to Rainbows 220), and crit rate of 90% (Rainbow's crit chance is 70%). In order to obtain it, you'll need to defeat the Dream Devourer, let the credits roll, and create a new save file. When you start your next New Game+, Chrono will have the weapon.

Practically however, since Attack Power caps at 255, you may find other weapons with different effects to be more desirable once you're at a level of power at which you can acquire the Dreamseeker in the first place.