I've been doing freelance jobs lately that do not involve NDA. However I received an offer from a client that requires an NDA prior to project start. Does NDA projects restrict the project themselves from being put in my portfolio?
It very much depends on the content of the NDA.
Recently, I worked on a cutting-edge mobile payment app - and even without an NDA, it was pretty obvious that I (initially) was not allowed to mention it. However, after the launch, I could mention the project by name and elaborate on the technology stack.
Whenever in doubt, just ask the client. I usually send a sample description for them to approve, as that seems a simple and transparent way to avoid any legal pitfalls.
Uhm, YES. They are not allowed.
Non-Disclosure means you can't tell anyone what you worked on. That includes showing it off in a portfolio.
If you would like to display the work in your portfolio you need to specifically discuss that with the client and get an written addendum to the NDA which specifically states what you can display in a portfolio. But I can't see any clients being okay with "Keep our secrets... but show them off in a portfolio".