Will,
Trace elements are like vitamin tablets. Yes you need them but do you think you could live on vitamins alone? Think about it for a second - that's why they call it "Trace" elements. Plants only need a trace. How much Iron, copper, or zinc or manganese do you think any living organism can swallow? Not a whole lot. Now think about the building blocks of life - proteins, enzymes and nucleic acids and so forth. What are they made out of? How about Nitrogen (N) combined with Carbon (C) to build chlorophyll, DNA and RNA? No nitrogen no DNA, no chlorophyll - no plant.
Think about how living cells are powered. They need a very active ingredient like Phosphorous (P) which is so active it glows in the dark. It's so active we use it in light bulbs. Plants use Phosphorous the same way we do in a lamp. It's used to transfer energy by electron movement. When there is insufficient Phosphorous this is like having a dim light bulb. No energy, no plant.
Potassium (K) is also a very energetic metal. Plants use it as a catalyst in the myriad of chemical reactions that are constantly occurring within and between the cells.
So plants need N, P, K and C in the same way and in the same relative quantities that you and I need meat and potatoes.
Given the right quantities, TPN+ will provide the plants with NPK so they will stop dying of starvation and eventually that will arrest the formation of algae. The dropchecker filled with 4dkH water will help you to ascertain how much C you are injecting.
Asking how much TPN+ you will need is like asking how much food you will need. As long as you want the plants to live you will constantly need to feed them so after the 250ml bottle of TPN+ is empty in a month or so you'll need to buy more. Yes, I consider the price very steep, and that's why I suggested that you buy the dry powders to make your own TPN+. For a little more than that £10 for the 250ml bottle of TPN+ you can buy the raw ingredients and make almost a year's supply of homegrown.
The photos aren't real clear but it looks like some BGA mixed with Oedogonium and maybe GSA. I'm not sure but whatever they are it's a sure bet that they are there due to extreme starvation so at this point I don't really care what they are.
The bottom line is to get your plants fed by hook or by crook. If you want to save money then you'll have to study that dosing article I gave you the link for and ask further questions if any of it is unclear.
Cheers,