The sentences are all correct. As for the difference between the two, most of the time they mean the same and can be interchanged. The 2nd of your sentences shows a good example of when they do differ a bit. "Proceed" is often used when there is a certain set or sequence of actions and you proceed from one step to the next. "Continue" can mean that only one action is done for a period of time. Hope this helps you :)

Maybe it would help if you look at the synonyms for proceed and continue. Here is a good link: http://www.thesaurus.com/

There is very little difference between the two words. They both mean to move on to another topic or activity. You can use either (both) in most cases and be totally understood. Continue is a bit more commonly used. Proceed is slightly more upper class (snooty) But acceptable.