Take your time and slow down!
The start is the most critical point.
You are technically cycling yes, but you are cycling for freshwater... And only if there is something dead in there to decay and add ammonia. Its not the same bacteria as saltwater (or so I think, I've understood it to be once you've lowered the salinity enough it kills the bacteria, someone correct me if I'm wrong!)
What I would suggest is dump that tapwater out, and get some good RODI water. You CAN keep the tapwater. You'll thank yourself down the road if you dont. Even if you still get algae/cyano/etc issues, you'll be able to rule out tapwater as the cause of your problems, otherwise you'll never know if its because of the tapwater, or if its high nitrates or something else!
As was said above, take your time. You can cycle without a light, thats actually preferable. A light in the early stages just promotes unwanted algae growth. Until theres coral in the tank, you don't need light. Even fish can be fine with just ambient/room light! My QT is run lightless so they don't get as stressed.
Read up on what you want before you buy a light.

The type of corals you can keep, if any, will greatly depend on that.
Best of luck!