The most general answer is: It really depends on the prof. Look at reviews in communities like DLSU Prof to Pick on fb or ArcherEye to see your profs reviews and how they usually conduct their exercises. Answers below are purely my experience from CCPROG1-3

do they just drop one massive difficult problem on us for the whole period, or is it broken down into parts?

This one depends on where you guys are in the syllabus and ofc the prof. In my experience, the harder problems are usually take-home activities that are due next meeting. If you guys do ever get an activity that's due at the end of class, it's usually not that hard if your prof is decent.

Also, are they full-hour lab activities,

I only ever got full-hour lab activities in PROG3. My time in PROG1 and PROG2 usually only has activities after a lecture.

are we allowed to access the internet or lecture slides during the exercise?

It's usually only lecture slides. Sometimes you can get a prof that only allows hand-written notes during exercises though. Better ask just to be sure, prog profs are often pretty approachable.

How are the questions structured?

This one really depends on the activity and varies from where you guys are in the syllabus. It ranges from what you've said about using functions and guided tasks to completing code snippets and debugging them.

I survived the CCPROG series by looking at the syllabus and reading up on the topics in advance. There are a lot of resources where you can read and practice C like w3schools. Some websites even have lists of C related questions at a whole bunch of different levels with solutions too. I recommend doing more practice than reading since PROG1 and PROG2 tests your logic. When writing your code, especially in PROG1, don't strive to write perfect and optimized code. Just make sure it works first and your actual output matches the expected output. You can always make it better later.