yes, CL alone will kill the algae- polyquat works good to prevent, not so good to kill algae
at your CYA levels, you need to maintain 20ppm FC to shock the pool- maintain as close as you can 24/7 until the pool passes overnight FC drop test- lose <1 ppm FC overnight, and have <.5 CC ( TC - FC )
Can't guarantee completely gone by Sunday, but that's the right track!
you also need to get your pH up some- 7 is really pretty low- I'd add enough borax to bring the pH up to 7.4, shock the pool, then straighten out the rest of the numbers...
The bubbles are some residual from antifreeze or some reaction with oils... the shock process should oxidize that as well I believe...