Yeah, you can download them at any stage; you just can't play them until post-Ch25.
It uses all of them, even if they refer to the same stats: if a character has Rally Speed, Rally Love, and Rally Spectrum, nearby units will get +10 Spd and +6 to their other stats. Worth noting that while you can stack multiple different Rallies that affect the same stats, you can't stack multiple of the same Rally: using Rally Speed a second time with another unit won't add an additional bonus.