These are NOT correct, complete English sentences. However, in a list of "bullet points" they don't need to be. I think what you have written for the first five points is correct and acceptable, and that starting each objective with a capital letter and ending each of them with a period is good style. I don't know whether there is any official style guide for bullet point lists. I do not like your sixth bullet point. It is not a parallel construction with the others, and it is not an objective. I think it should be a regular line of text without a bullet.

Yes, you can. But you have to finish your sentence when you start it with "to" . Let me use when of our sentences as an example. When you say this : (To Transmit and share knowledge about the oil industry through renowned faculty members and professionals. ) you can put a period or a dot. It has to continue to make sense. So after the professionals you have to say something like..... Professionals, (comma) is good. or (comma) is bad . You might be wondering how can I not add more and keep it the way it is (almost) take out the "to" at the beginning and it will be complete. Your options are : Transmit and share knowledge about the oil industry through renowned faculty members and professionals. (This sentence is instructive, it is telling people to do something. An order.) To Transmit and share knowledge about the oil industry through renowned faculty members and professionals, is what we need to do . (This sentence is now complete. It is an informative sentence. It is teaching people about something. )

I would say yes, you can, in the context of a project's objectives. Universities should have a small 'u' unless it is the name of a specific university. For example, Florida has x number of universities one of which is the University of Central Florida