generally, will older hdmi cable support deepcolor and other hsmi 1.3 transmissions like 1080p/24?

just wondering if i should run a new hdmi "high speed" cable to my hdmi 1.3. projector.

does "high speed" signify anything?
what hdmi wire to i need to support hdmi 1.3?

This is a matter that I've seen debated both ways. Basically, an "HDMI v1.3" cable differs from an "HDMI" cable mostly in the way its tested. On longer runs, that may make more difference (especially when pushing 1080p out to a projector), but in general my answer to the question of "do I need a v1.3 cable?" is "no."