The SMV file is the input sequence that was used to beat the game like that. You need the correct version of the emulator and the ROM to play that back, in this case this is:
The emulator "snes9x-1.51-rerecording-svn-r51" from
Here
And
The ROM "Chrono Trigger (U) [!].smc", this I cannot link you to because it is against the rules.
You should be able to find the information regarding which emulator and ROM to use in the Submission or the Discussion Thread (linked in the submission) for every movie. There are a couple of submissions that do not have this information, they are usually a bit of trail and error to figure out.
The emulators are usually found in the Emulator section of the forum if they are not linked from the submission.
The filename of the input file is different depending on the emulator that made it, movies for other system have other extensions. (I.e. N64 have M64 as the extension)
I hope this answered your question, if not, I or someone else will try again.
You can re-use this thread for the other questions, that should be no problem at all.