Q1: Why does the sending to port 25 - not secured by SSL/TLS! - lead to Exchange sending its internal certificate to the client?
By default Exchange uses Opportunistic TLS:
Exchange would always first try to establish TLS connection with the client.
If the connection fails, Exchange would fall back to not using TLS.
Since TLS connection needs a certificate and the Exchange self-signed certificate was not trusted by the client, it caused the TLS connection to fail, thus the connection did not use TLS.
Q2: If the server does really need to use its certificate even for unecrypted connections on port 25 why didn't it use its "real" configured certificate from my local CA?
Have you configured the server FQDN (mail.contoso1.net) on the receive connector (Default Frontend EXCH1)?
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