You CAN stock the tank with hardy shrimps such as Red Cherry Shrimps and see how it goes, start off with a small number of them, say 6 or 8.
I usually recommend a established tank thats been up and running for at least 3 months before adding shrimps, but of course this is not always feasible.
Personally I did add amano shrimps into a new tank thats was just cycled, theyre fine BUT i did have nitrate issues and had to do quite a few water changes to keep the levels down. Now after a few months, tank has settled somewhat and shrimps are fine, even getting berried amano shrimp as well.
It helps to know what signs to look out for if the shrimps are not happy, rushing around the tank, looking for 'safe' spots or even trying to climb out of the tank (thats in extreme cases) is a sure sign they are not happy in the water for whatever reasons.
Copper is not good for shrimps at all, or for snails either actually. Too much copper wlll likely kill them
Having said that, shrimps and snails actually need a tiny trace amount, really minutae amount of copper for normal body growth.
Liquid co2 is not really recommended, personally have not used it myself, but i do add fertilisers to all my tanks and not had any issues but I do check the ingredients if there is anything potenially harmful such as copper or metals.
Root tabs tends to be fine, as these stay under the substrate and get consumed by the plants themselves, I use seachem flourish root tabs in all tanks btw and all my tanks have shrimps. As long as you do not disturb the substrate or move plants around too much thus exposing the root tab and debris intot he water column, should be fine.