As I understand it, when I buy some tokens, their price already includes that ADA bound to them? So, for example, each token_name has like 0.01 ADA locked into it, right?

I just don't get how this amount of ADA could be different depending on number of tokens in the same transaction

Each transaction output has to be at least 1 ADA, anyway. If it contains native tokens, this rises to something in the range of 1.20 to 1.40 ADA (it depends on the length of the token name).

And, yes, services selling or giving away tokens tend to request you to send an appropriate higher amount upfront to cover this.