Hello Jirka,Ahoj Jirko! Glad to see another guy from Slovakia here
1. I guess the safest way how to answer this is to use water tests. If there are plenty of healthy and fast growing plants and NO2 is zero and NO3 low enough for a few days, it should be safe to add livestock. One has to be careful with soils containing high amount of artificial fertilizer. Nitrate respiration might occur (NO3 is converted to NO2) after few days after soil submersion. Waiting for months is a bit overkill, even if it's a safe bet (although, depending on the soil used, you might starve your plants). For impatient people it's a good idea to have selective ion resin (Szat clear water in our region) at hand and use it in emergency when NO2/NO3 is too high.
2. I think that Diana's recommendation is good. Plants which grow like a weed in one tank will just slowly die off in another. Providing an abundance of species will ensure that at least some are going to get a strong hold in the tank. It is expected that maybe only half are going to survive and spread across the aquarium (but you can't really tell which ones exactly in advance). E.g. I had an extremely good success with Sagittaria subulata in one tank, yet it won't grow at all in the second one, no matter what I do.
3. I tried to run a nano tank without a filter. Technically it worked absolutely fine, yet I noticed increased growth of plants and more lively behavior of fish with a little bit of water movement. I believe that filter in terms of biological filtration is not essential, but water movement is beneficial to plants and livestock as well.
Just my 2 cents
Sorry, I didn't get to your questions sooner. Honestly, I think that Mysiak answers your questions here beautifully--probably better than I could.
Welcome to APC!