New tank problems - beware long

I cannot get my tank to cycle and am lost at what to do next. Have a
30 gallon tank with several fish in it. I have been receiving
conflicting info from books/fish store and I think I have it all
screwed up. Been messing with this for a couple of months.

Right now the water is very cloudy with a green tint. It has been this
way for 2 weeks. I have resisted the urge to do a water change but it
is looking terrible. I was hoping this was the late stage of cycling
but I'm not seeing any changes. Algea is growing on the sides of the
tank. Ammonia=4ppm,nitrite=0,nitrate=0.

Fish store said I was under-filtered. I had a whisper 30. I got rid
of that and put in a emperor 280. It has been several days an no
improvement. I have used cycle. I have used something that came in a
packet that had to be refrigerated (can't remember the name). Still no
luck.

Questions:

Planning on doing a 20% water change today and vaccuming the gravel in
hopes of clearing up the water. Good idea?

Are water changes detrimental to cycling?

The emperor 280 comes with a media basket. Should I put something in
there?