Colleges in USA

You should have a post-graduate degree with at least55% of marks for general category and 50% marks in the case of SC/ST category or equivalent CGPA in the concerned subject or in an allied subject or any other post-graduate degree recognized by the University as equivalent thereto.
In addition, you should be In-Service satisfying the above eligibility conditions to be able to apply for part-time. Admission into part-time programmes will be made in the specified order of priority as given below, with service seniority in each category:
Teachers working in the University or the A.U.P.G. Centres. Teachers working in Post graduate and professional colleges (not applicable if you are teaching Physics, Chemistry, mathematics and Humanities in professional colleges) or, Lecturers / Librarians / Asst. Librarians working in affiliated degree colleges teaching physics, chemistry, mathematics and Humanities in professional colleges or Teachers working in Polytechnic / Government Junior Colleges. Technical employees working in research institutes attached to Andhra University / Non-Teaching employee of Andhra University, A.U.P.G. Centres having completed at least five years of service.

Yes,
This is not a required criteria. But, it is definitely good to have a work experience. It shows maturity, skill, thought process, research mindset, amongst others. Needless to say, relevant work experience is better than irrelevant. But, some is better than none. Just work on remaining constraints.
Let's take a look at where each piece of the puzzle fits in. I will break it down into 2 categories:
Quantitative:
Aspects of your application that has numbers; that can be measured like your grades, GRE and TOEFL scores.Grades:
The higher, the better. But, it is not the end of the world, if you don't have a CGPA above 7.0 or 8.0. Why? Because of the other aspects of your application. GRE Again, the higher, the better. Beyond a certain score (330+), it doesn't really matter much; your amongst the best students. Now the other qualitative aspects of your application come into play. Below the universities minimum score, your application moves to the Stand-by pile.
TOEFL: Most international universities require it if your first language is not English. Some universities/graduation programs use a high verbal GRE verbal score as a substitute; do your research before taking the TOEFL. Meet the minimum criteria listed on their website and you'll be good. SOP: Some professors say this doesn't matter as much. Some professors read through them briefly, while some others place a greater emphasis on SOP.