I know your original post was about the algae concern, but I wanted to comment on a few other things:
I agree with BBradbury above: Generally a larger volume of water is better for aquariums. Small volumes of water can be sensitive to changes in the tank environment such as temperature, water chemistry, and toxins from the bio-load. The lighting is also a bit more difficult to get right over a nano tank. However, the up-side of a small volume of water is that water changes involve less water (which is sometimes attractive).
From experience, I've also found that planted nano tanks are quite a challenge because almost all aquatic plants grow too big and fast for the nano sized tank. If you get good at growing plants, you will constantly struggle to maintain the aquascape aesthetic in such a small tank.
There are many philosophies regarding aquarium-keeping and your use of the gravel vacuum tool stood out to me. I'm not sure if you have a particular aquarium-keeping philosophy that you adhere to. Personally, the gravel cleaner is something left over from the (my) past. In a planted tank with an appropriate substrate, a gravel vacuum shouldn't be needed. In my case, I use soil which is sometimes capped with a fine-grain gravel. You can imagine that using a gravel vacuum would make quite a mess in that case.
To me, the gravel vacuum is an icon of the general idea that everything needs to be clean, clean, clean. You need to be careful with this concept and be mindful of the micro life that you will also be establishing in your tank. This dictates how you maintain your substrate and also how you maintain your filter and associated equipment.
You say that you are new to freshwater tanks, so perhaps you will adopt new philosophies over time. I would guess that the brown algae you have has its roots in the particular manner in which you are keeping the tank.
- If you feel a need to clean the gravel, perhaps you are overfeeding - Where is all the excessive buildup coming from?
- Others have pointed to overstocking, and I agree.
- You also may not have enough water movement/flow. (This is another area that is difficult for nano tanks.)
- You may also not have enough biological filtration depending on what kind of filter you are using.
- Your substrate may not be appropriate and the gravel size too large (but you don't want too small either, i.e. sand)
There are many things to get in order to avoid the various algae types. Hopefully, this will give you a few ideas on what to research further... There is a lot to learn, so I didn't want to try and throw it all at you at once.