algae in uncycled tank that I want to cycle

So I've had 3 plants thriving in my tank. I've been wanting fish since I started the tank. After a few disasters, I decided to totally switch it up so I swapped gravel for sand (and flora max) and fake plants for live.

Since the ultimate goal is to have pretty guppies in there, I began trying to cycle it again. I could not find bottled ammonia anywhere, I chose the frozen shrimp method. It took at least 2 weeks for the ammonia spike (it's only a 10 gal) and it's taking another 2 weeks to go down again. It is still high- between 1 and 2ppm. Still no nitrites at all.

My tank is filled with algae and no critter to clean it up. I wanted to get some ghost shrimp in there but I know they won't survive the ammonia level. When I siphon to try to get it out it obviously just sucks up a bunch of sand. There is both green and brown algae in there. What do I do?

To cycle my tank what do I do? Put the shrimp back in once the ammonia goes back down? (Someone told me I'd have to put it in and out a few times, but with how high it spiked I'm scared it's too much ammonia for the nitrite to form therefore if I put the shrimp back in, it will spike too high again..)