Although one bag of shock does treat usually 10,00 gallons, that is assuming a clear pool to start with. Since you had an algae infestation, more shock will be required. A simple rule of thumb is when treating problem water to double or even triple shock the pool. Simply put, there wasn't enough shock there to finish the job. Test your water for chorine. Most shocks are chlorine based. If your chlorine is low or zero, it will confirm the need for more shock.
The bigger the cartridge the better the job it does the size you use would depend on the load you expect it to have to handle. speak wit a local pool professional for the best answer. The smaller the cartridge the more often you have to clean it.
u can use a aqueon 55 gallon filter
I think you should go for a cartridge filter (Pentair 320 sq ft - we can supply for $600 incl frt). Cartridge filters are much better than they used to be, and are far, far more coinvenient than sand. Suitable sand filter would be approx 100 sq ft (and same cost as 320 sq ft cartridge).
yes you can it will be fine. i have experience :) haha
For a few days yes.
I would highly recommend it, yes
Clean filter
1 gallon, with a filter change.
You may be able to use a very small internal filter with a 2.5 gallon tank. You can check with your local fish/pet store and they may be able to show you ones that would work for your tank
Air bubbles will do nothing. What is needed is a filter.
It never hurts to have a filter it will only improve your fish's chances of survival and decrease your need to clean.
A 300-gallon filter? I have no clue. The industry rates filter on the diameter of the filter tank. So if you can cover the gallons to inches I can tell you how much sand you will need.