Don't worry about the algae for now - it's very common to get "algae blooms" while the tank is still cycling. In fact, it indicates you might be approaching the final stages of the cycle. What are your nitrite and nitrate levels? What test kits are you using?
pH is okay at 8.0. Ideally, you want it in the 8.0-8.4 range.
The purple on the rock is good - it means you have good calcium levels.
Things are going to be a little bit unstable while the cycle completes. Sometimes, a tank can cycle in as little as 4 weeks, and because of the cured LR you have in there, you might be lucky and it sped it up. However, don't get anxious. Make sure it has cycled all the way through because otehrwise, when you start adding things in, you are going to disrupt the cycle and prolong things even more.
That means you have at least a week to go, maybe up to 3. You are almost there
When they cycle completes, do a 30% water change, a 10% water change a week after that, and you are ready for your first addition!
So now is the time to start thinking what you want to add. Fish? Coral? what kind? Whatever you decide on, add one specimen at a time, meaning add one thing, give it about a month before adding more. start small - as a rule of thumb, only keep 1"/gallon (if your tank is 10G and you have 10lbs of LR, you are going to have about 6-8g total water volume, so all your fish should total less than 6-8" in length). when you start adding living things, be ready for your water parameters to get all out of whack and fluctuate during the first few weeks. This hobby is all about maintaining a balance, and every change (adding something, removing something) starts a chain reaction that unbalances everything. Sounds overwhelming, but after you get the hang of it and making less changes, it's not bad at all.
If you are going to do coral, there are different types: soft corals (LPS) and stony corals (SPS). LPS or "softies" are easier to keep and more forgiving.
Also keep in mind the restrictions of your tank size and research your intended purchase to make sure it won't outgrow the tank.