Do professors work all day correcting papers and communicating everyday to students 24/7 when working a salary ?

Sure if they love their job

You are Joking

Well no, not 24/7. No one does that.  But professors DO absolutely work a 40+-hour work week, and do significant work at home (even before COVID).  They teach, prep for teaching, grade papers/assignments, hold office hours, have meetings, conduct research, have do work on writing up their research, etc.

Professors at universities are promoted and given raises mostly based on their research and publication. That is what builds a university's reputation. At 4 year colleges and community colleges, teaching is the primary function of the faculty. That's why it's often better for students who need more personal attention and help to start at a community college or small 4-year college. 

Professors in science and math often give tests that can be scored by a computer. Faculty in the humanities spend more time grading and responding to written work. I've seen recent discussions online from faculty who limit the time they respond to email, and won't respond on the weekend. I generally to respond to students as soon as I see the message, especially if it's a question about how to do an assignment. 

of course not.  no one works 24/7, even online.

While it's true that the majority of what all good teachers do takes place outside of the classroom, no teacher spends 24 hours a day working. Assistant professors and tenured university professors are given a set number of teaching hours per semester and enrollment numbers for each class are set at a manageable level that will enable each professor to do his or her job effectively. Most maintain set office hours so if students need to meet, they have to schedule a timeslot within those set hours. And while grading can be a tedious and lengthy part of the job, most professors who have been teaching for a while know how to manage their time so that they can get those things done in a manner that doesn't cause total and complete pandemonium in their personal lives. If a professor prepares his or her lessons beforehand, has good time management and classroom management skills, and draws up a solid plan for each class and sticks to it, getting everything done in a decent amount of time is usually pretty simple.  

No. They have a contract of employment with the institution at which they have a chair which specifies how many hours they work.