Question about cycling

Hi guys,

I have a dilemma that's puzzling me and hope that someone could help.

I'm currently in between week 2 and 3 of cycling my 60 gallon tank.

I have 25lbs of live rock, 40lbs of live sand.

I have been testing away. Here is what I have:

week 1: ammonia 0 then spiked to .25 after adding a raw shrimp.

Nitrites remained at 0, Nitrates at 0 on week 1.

Week 2 - ammonia fell back to zero, nitrites at zero, now nitrates are at 20ppm.

I have only about 35 gallons of water or so in the tank, I didn't fill it all the way up.

I have a hob filter running with biohome media and crushed coral after I read a lot of good reviews on the matter.

I have a ton of cyano algae growing on the rocks, two dead starfish, a dead snail, and an almost dead hermit crab that came on the live rock. The live rock is high quality from our local fish store.

Any ideas if this tank has already cycled?

I'm doing a 20% water change today.

Also, how can I clean my sand, a rusty type algae is growing on it. I have a Jeboa wp25 wave maker running and there is very good flow.

Thank you guys so much!