The ammonia is mainly due to the fish, it's their version of urine. Your first fish will have been excreting it from the moment they went into your tank. Unless you added ammonia in the 5 weeks before you got the first fish, you are still growing bacteria to deal with the ammonia and then the nitrite that the first bacteria make from the ammonia. Do you have a reading for nitrite as well as ammonia?
The fact that you have ammonia in your water suggests the tank hasn't cycled yet, that is it hasn't grown enough bacteria to remove all the ammonia made by the fish. And you may well also have some nitrite, which is why I asked about it.
You need to do a lot of water changes whever there is ammonia and/or nitrite in the tank - maybe even once a day, and more than 10%. Then once there is no sign of ammonia or nitrite, the usual water change regime is 25 to 30% once a week.
And if you don't have your own test kit, ask the shop to tell you the exact figures for both ammonia and nitrite. Just telling you 'a bit high' isn't very much help, you need to know exactly how high.
The algae isn't causing the ammonia, it's the other way round. The ammonia is causing the algae to grow.
Uneaten fish food and fish poo collect in the gravel and do decompose to make more ammonia. Those siphon tubes can take a bit of getting used to, though I never had a problem with them sucking the gravel up. Is
this what you have? It looks like the kind with a wide plastic tube with a valve at the top inside the blue bit and a length of plastic hose pipe attached to the blue bit. You immerse that wide tube totally in the tank (with the end of narrow hose in a bucket) then move the wide tube up and down quickly till the water starts to flow. You could always fill a bucket with water, stand it on some thing outdoors so it's off the ground and practise starting it with that - no fish to frighten.
The other way to start it going is to lower the entire thing into the tank slowly, starting with the wide end and making sure the water goes all the way through the tube and hose. Then hold the wide tube under the water with one hand, put the thumb of your other hand over the end of the hose, lower it into the bucket and take your thumb away. But once you get the hang of it, shaking the plastic tube up and down to start it is quicker.
How big is your gravel? When I had gravel (got sand now) it was quite fine but it didn't get sucked up. It would go into the wide plastic and swirl around but it didn't go into the narrow hose. To clean the gravel, I started the water flowing then pushed the wide end right down into the gravel, watched the gravel swirling round and the muck going into the narrow hose, then when no more muck came I lifted it up slightly so the gravel fell out and moved the tube along an inch to the next patch of gravel. Doing this every week meant I kept the muck to a minimum and could do the whole tank bottom in one water change. If you haven't cleaned the gravel properly you may find there's too much muck to get round the whole lot in one go at first - but you need to be doing lots of water changes to get the ammonia (and possibly nitrite) down to zero, so you'll soon get it all done. Once you've got rid of what's there now, it'll take less time to keep it clean.
I have never used an electric or battery powered siphon tube as the kind like the interpet one are so cheap. I did find the blue bit broke after a few years with 3 tanks to clean, but they are very cheap to replace.