brewing at home

I asked myself the same question. In my mind, each and every F1 is a batch, but, I would also think of the F2s in a way as a batch if I am using a different recipe and trying out different things. But I guess that because everything in F2 comes from F1, F1 is what counts as the batch.

If your kombucha has very little carbonation, I would say this would almost completely remove the carbonation entirely. So it depends how much carbonation you currently have. As others have mentioned, running kombucha through sieves and filters does reduce carbonation, the type of sieve does make a difference, and the sieve you have in your picture seems like a mesh one, which does reduce carbonation by a lot.

I believe that any time you pour a carbonated beverage between containers, you lose some of the carbonation because CO2 escapes. Pouring a carbonated beverage through a regular sieve causes CO2 to escape even more, and pouring it through a mesh sieve (at least it looks like a mesh sieve in the picture) will cause even more loss of carbonation.

So I would say yes, you are losing carbonation by using that sieve. If it's to filter out the fruits and what ever is in the kombucha, I would just do my best to have larger chunks that would fit through a regular wide holed sieve.

I count my F1 containers as 1 batch each. But I have heard of people counting their F2's as batches, since from 1 container of F1 they could make 4 different F2 flavors, each their own "batch".

I count each F1 as a batch. I usually have 2-3 F1s going at the same time, I count each of them as a batch, so that's 2-3 batches at once.