I will try to answer my own questions.

Can the messages in the heat-sending-transactions be read by anyone?
No, the messagee can only be read by the sender and the receiver (?).
The tag e2ee means end-to-end-encryption, so it should be encrypted.
What about the messages without heat-transfer, are they also stored to the blockchain?
Yes, they are all stored on the blockchain, therefore is the fee of the messages (?).