If you've used tap water and succeeded congrats!
I did it when I was a newbie in a 10 and a 20 gal, both were disasters until I was told to switch to RODI. I couldn't afford a system but started buying Culligan and things went uphill IMMEDIATELY.
As for the algea... You seem to have green cyano and bubble algea. Lights out works pretty well for cyano but it seems to be more of a bandaid IMO and comes back fairly qick without finding the reason behind the growth. I have been told to use chemiclean which is apparently fantastic.
For the bubble... I LOATHE the stuff. I had an outbreak and followed the advice "don't break them the spores will spread buy emerald crabs" which is sound advice but when it comes to the point that it covers EVERY inch of the rock, overflow and starting to grow on the sps... grrrrrrr... I gave up and scrapped everything I could reach and did a water change at the same time. The 4 emerald crabs could keep up with it afterwards but I still scrape at it during water changes.