'Misgiving', often used in the plural, means concerns. If you have misgivings about something, you are doubtful or worried about them, and you think they will have bad consequences in the future. The Cambridge dictionary has this example: 'Many ​teachers ​expressed ​serious misgivings about the new ​tests.' 'Disquiet' is more of a general feeling in a place or among a group of people - it's an atmosphere of unease. It's also quiet a rare word. I've never used it. 'There's no + gerund' is a fairly colloquial way of saying 'it's impossible to'. Here's another example: 'Are you sure you want to do this? Because if you decide to do it, there's no going back.' = It's not possible to go back.

Tip: when you ask about differences, the question form is "What is the difference between ____ and ____?" We never use "of" in this question.