Are these chainrings the reason my chain skips/hops? When I ride my bike normally, then chain skips like crazy. I know it skips in the front because I stuck some paper in the chain to see if it moved and it didn't.

Chainrings:
The large chainring in the picture looks very worn out. Usually by the time teeth on a ring are "shark-toothed"- or very pointed- the chainring is completely shot. However, it's likely that unless you've been replacing your chain regularly that all the other drivetrain components (chain and cassette) have been worn beyond use as well.
You should get a chain gauge and a cassette gauge to check this, or go by your local bike shop as they should have both tools. Chain gauges are very reliable tools for measuring wear. Cassette/sprocket wear gauge measurements are usually to be taken with a grain of salt. If your chain is completely hosed you can bank on needing a new cassette as well. If it's worn out without being beyond expected tolerances for a worn chain, you might try replacing your big chainring and your chain and see if you get any skipping in the back. If you don't, good for you and enjoy your ride. If you do then replace the cassette as well.
Next time, before your chainring gets as worn out as it is, you can check chainring wear by visually inspecting "chain lift" off of the chainrings. This is especially useful when changing to a new chain on used chainrings. Chain lift is the amount the chain rises out of the dips in the chainring under torque. Hold your back brake, and while off the bike step on one pedal at a 3 oclock position. Look to see if the chain appears to be coming off the chainring. This will be a useful trick if you want to try to save your small chainring, which doesn't appear to be as worn out as your big one.
In the future, check your chain's wear monthly if your ride occasionally or weekly if your ride nonstop. Changing your chain when it needs it will increase the longevity of the other components that come in direct contact with the chain- most importantly your chainrings and cassette sprockets.