"I possess a degree"is very formal, probably too formal for today. For any situation, even when you are applying for a job, you can simply say, "I have a degree in [subject]."
By the way, I think it's great that you looked this up on Google. Google can be a great tool for questions like these! You can also use Google to get ideas about which verbs are more frequent. For example, on my computer, "I possess a degree" gets 290,000 pages which is a lot. But "I have a degree" gets 34 million, which is really a lot!
an idea turned up - when I have a nice though suddenly: Yes, exactly
make a lot of efforts: This is fine except it's "effort" (no S). "A lot" is fine.
You could say that your favorite pastime (not amusement) is going to the theater.
Instead of "romantic idea," you can just say "I have a dream to live in the mountains."
"Visiting professor" or "visiting lecturer" is better than part-time teacher. Part-time only refers to the number of hours of work per week, not how long you have been an employee.
"What I am worth" usually relates only to a job or an employer. You can talk about "my self-worth" -- this is closer to your meaning.
I am eager to witness this performance: This is fine if the event really means a lot to you. But be careful, people sometimes use this expression sarcastically when they think the performance is going to be a failure.
Grades of your diploma do not do credit to you though I am still proud of you: As Jura said, I think this should be "your grades do not do you any credit" or "your diploma does not do you any credit." A diploma usually doesn't have grades on it but you could say "the grades on your transcript" or "the grades on your report card." A transcript is a document that shows all of the grades you received at your university or (perhaps) your secondary school. A report card is what children get at the end of each school term.
