Is one-time pad encryption vulnerable when near identical data is sent many times with different OTP? Let's assume a text file that grows at its very end but is otherwise not edited. We now have 100 transmissions of this, but OTP-encrypted (different OTP each time, of course). The first 50% of the original file are identical.

Of course nothing can be said about the other 50%. But can parts of the first 50%, which stay perfectly identical, be attacked?

(Please be light on the lingo and math, I'm a noob.)

Different scenario, same question: The text is edited in various places, but only individual sentences. This shifts the bytes around, but apart from that, most of it stays perfectly identical.
No. As long as each pad is completely random and independent, you can encrypt literally anything of the appropriate size (no larger than the pad) and retain information theoretic secure confidentiality. This attack is termed a known-plaintext attack, or KPA. The OTP encryption scheme is only vulnerable to this if you re-use padding material, which breaks the scheme. A proper OTP is not vulnerable to KPA.