How difficult it would be to convert OPT to F1 for Fall 2018 ?
( Cannot say anything about H1 and Part Time PhD option , because I cannot depend on a lottery to judge my future)
As of now, it is not difficult. You can always change to F1 from other visa types. The story has to be of course credible. If your OPT helps you recognize that there is bright future in a certain aspect of the research that you want to pursue, that could be a very good reason, for example.
Is it good to do 2 degrees (in my case MS and later PhD) from same university ? I have heard that employers , even for professorship, look for diversity of experience and getting degrees from different universities are always preferred . How much truth is there in this statement ?
That is not an over-riding criteria in what will follow your PhD. Is your research useful? Is it in a new breaking area? cutting-edge? Good publications? Is your professor's Lab well known? What is the track record of placement among his/her doctoral graduates, etc. These are the key questions.
Is it worth the effort to look for other PhD opportunities in other universities too ?
One of the lessons that I have learnt in life is to go for the best that you can get into. You always have to take a risk. Homo Sapiens succeeded in conquering this planet because they always took risks. Not sure if Neandertals vanished because of their lack of risk taking?
At any rate, you will ahem time next year to redo GRE and get yourself in a great program. I will do that, if I were you.