Is Compensation for senators set by president?

no

The U.S. Constitution, Article I, Section 6, Clause 1 state, in part,

"The Senators and Representatives shall receive a Compensation for their Services, to be ascertained by Law, and paid out of the Treasury of the United States."

And the 27th Amendment to the Constitution states,

"No law, varying the compensation for the services of the Senators and Representatives, shall take effect, until an election of Representatives shall have intervened."