You have two (unrelated) questions here, from what I see.
Firstly, the Ntirite spiking from culling duck weed has no relation to your TDS reading.
Are you using RO (or that zerowater water jug) right? -> there should be no nitrites in that. So it mean your beneficial bacteria in the tank cannot cope, which mean not enough of those little buggers.
You shouldn't be getting Nitrite spikes in a mature (cycled) tank. How much biological filter media do you have? How old is the tank?
Don't clean out your filters or gravel vac too often. Once a year is more than enough. The idea here is to get your tank mature enough that beneficial bacteria load is high enough to deal with an imbalance like culling some duck weed. I'd suggest bacteria in a bottle, but I cannot guarantee any of them will give you the right type of bacteria to tackle nitrites. Best to let nature take it's course here. Let them grow by providing the best conditions. Lots of oxygen, correct temps and food (ammonia). Ammonia is taken care of by the shrimp's waste and food. So you only need to ensure there is enough oxygenated water and don't let temps fall too low. Keep temps between 22-23 degC, that's for the shrimps. Make sure the water surface tension is being broken by air stone bubbles or by your filter outlet.
Secondly, with TDS ... since you have cherry shrimp, I would personally aim for 250TDS water change each week, and slow drip the new 250TDS water back in. At 10% water change, this can take a while to get 350TDS down to somewhere near 250TDS. Once you reach close to 250TDS, switch to 200TDS water changes. And maintain between 200 - 250TDS from there on.