Master Slave Replication in Mysql
The simple answer is No.

In Mysql replication, Master copies the bin log files to slaves, and after that, it's work is over. Now the Slave will run the bin files and execute them, but there won't be any performance on Master.

There might be scenario where you are using full synchronous replication, in which master will wait for the slave to execute the query, but again it won't impact the performance in terms of memory or CPU, but the master will wait for the query to be executed.

Also, for your second question, Phil already answered it, that ssh sends data through encryption which uses a lot of CPU, hence if you want other ways, use the other methods which are described by Phil.