Hi,
I can answer this for you.
When you say:
Is it possible to make certain fields required in Events Calendar Pro?
You mean in the event editor in the dashboard, correct?
We do not have that feature, but you maybe able to use some Javascript to require fields.
Here is a good article on Data Validation using jQuery that may help.
http://speckyboy.com/2009/12/17/10-useful-jquery-form-validation-techniques-and-tutorials-2/
Also, if you think that is something you would like as a feature I encourage you to visit our User Voice Page and either upvote an existing request or make a new request there.
http://tribe.uservoice.com/
Let me know if I did not read the question correctly or you have additional questions.
Thanks