Hey there! Yea, I would say that your tank is a little overstocked. Usually, with neon tetras and guppies, you want a minimum of 5 in each group, and 3-4 cory cats. Also, with your pleco, it'll need a much larger tank as it grows older, as they can get up to 2 feet in length! If possible, I would move the beta, corys, and the pleco to a larger tank, get the group of corys up to 4 or so, and let the neon tetras and guppies keep the 10 gallon, as since your guppies are pregnant, it'll be a less stressed environment as they have more room. Hope this helps! And for the air pump and air stone, no, its not really necessary if you have good water flow from your filter, but it does help aerate the air and gives better water circulation. Plus some fish like to play in the bubbles of the air stone, so its pretty fun watching them do that.
Honestly, I recommend the API liquid tests. They're a bit pricey, but totally worth it. You can get the master liquid test kit off of amazon for 21-25 bucks or so, so its quite cheaper than in a LFS.
Do you have any plants or a picture of your tank setup? Shrimp in general prefer heavily planted tanks, as they like to pick off algae thats growing on the plants. Hope this helps, and good luck!