Do not ever hit a cat or use any sort of physical punishment. You will only teach your cat to fear you.
For chewing, try spraying Bitter Apple or Bitter Orange (there are formulations specifically for use on plants) on the leaves. Dusting cayenne pepper on them may also help. You may wish to grow some grass or catnip for them as an alternative; plants do provide them with needed nutrients (the absence of which may be causing their grazing).
For digging or urinating, cover the dirt with aluminum foil or gravel. If the plant needs it, add some vinegar to the soil to counteract the ammonia in the urine.
There is a myth that cats will kill babies. The superstition is that they'll "steal" the baby's breath; the latter day explanation is that they will lie on babies and suffocate them. While cats may like the baby's warmth and may curl up next to it, it will not often lie on the baby and in any case will move when the baby begins to flail its arms and legs.
Most cats are trustworthy around babies after getting over any jealousy, especially if it is trained not to use people as toys; however babies should never be left unsupervised around any animal.
You must remove the odor from items that the cat sprayed on to prevent the cat from using the same spot again later. The ammonia smell tells the cat that this is an elimination spot, so never use ammonia to try and "remove" the odor!
Cats sometimes spray to mark their territory so sometimes an area for your cat that other animals cannot go to will help. Keeping the litterbox immaculate will help in other cases.
Sometimes cats pick small throw rugs with non-skid backing to urinate on. This is caused by an odor from the backing that somehow tells the cat to urinate there (probably an ammonia-like smell). Cat-repellent sprays or washing the rug may help; you might just have to get rid of that rug. <
Pepper (black, white, or cayenne) can be applied to furniture and plants to discourage scratching. This does not deter all cats. You can also cover areas with double-sided tape (sticky on both sides) to discourage unwanted scratching. (Always be sure to provide an alternative scratching item.)
In general, cats will either use a post a lot or never use it. The deciding factor can be the material that the post is made out of. It has to be fairly smooth (cats usually don't like plush carpet) and shouldn't be a material that their nails get stuck in. Once that happens, they may not use the post anymore. Natural fiber rope wrapped tightly around the post appeals to many cats. Some cats like plain wood; a two-by-four made available may work well. Other cats prefer the kind of "scratching posts" that are horizontal rather than verticle.
Do NOT ever try to discourage a cat's mistakes by rubbing its nose in it. It never worked for dogs and most certainly will not work for cats. In fact, you wind up reminding the cat of where a good place to eliminate is!
Potential CAUSES for failure to use litterbox:
Vertical blinds can work very well; cats cannot climb up them, cannot shred them, cannot shed on them, cannot be bent the way horizontal blinds. It is furthermore easy for cats to push them aside to look outside. Vertical blinds are usually vertical strips of plastic, but they can also come covered with different fabrics to match your decor. These kinds are still pretty indestructible.
This will work on other chewed items, as well, although you will need to check the compatibility of the chewed item with the substance you put on it.
Another way to prevent this is to store the garbage can out of reach, such as in the cabinet under the sink or in a pantry where the door is kept closed. If the cat can open the cabinet door, get a childproof latch for it.
If the problem is one of tipping the container over, several bricks in the bottom of the container may help stabilize it. Once the cat is convinced it can't be knocked over, you can remove the weight.
These same techniques will work for other surfaces like dressers, TV's, etc.
The cat may simply be hungry and demanding its food. By feeding it when it wakes you up at an ungodly hour, you are simply reinforcing its behavior. If this is why it's waking you up, you can handle this either by filling the bowl just before you go to sleep so it will not be empty in the morning, or by ignoring the cat's wakeups and feeding it at the exact same time convenient to you every morning. The cat will adjust fairly quickly to the second.
If it is trying to play, there are again several tactics you can try. If you make a practice of tiring it out with play just before bedtime, you can reduce its calls for play at dawn. What works in some cases is to hiss gently at the cat. You can also try shutting it out of the bedroom. If it pounds on the door, put it in a bathroom until you wake up.
In persistent cases, try the vacuum cleaner, eater of noisy kitties. Go to bed, leaving him out in the hall. Position the vacuum cleaner next to the door, inside it. Plug the vacuum in, and arrange things so you can switch the vacuum on from your bed (eg, wire a switch into an extension cord). Wait for the scratching and wailing at the door. Turn the vacuum cleaner on. If cat comes back, turn it on again. The cat will eventually decide to stop bothering you in the morning.
If you have a swing-and-shut door, you might try a cat door to allow the cat access. A child-barrier that lets the cat jump over but not the dog is another possibility. Or a chain (like the chain some front doors have) might work.
A solution with closets that have double sliding doors is to drill a hole through the area of overlap, with the doors positioned closed or partially opened as you wish. Then you can use a nail or a peg in the hole to keep the doors in position.
As a cat owner, you should consider ways to minimize your cat annoying your neighbors. You could keep your cat inside when you are working or gone for a long time, supervise your cat when outside, bring it inside at night, etc. All cats allowed to roam outside should, of course, be neutered.
If the cats involved are owned by your neighbors, you might try a non-confrontational approach -- let them know what their cat has been doing and suggest that perhaps neutering their cat might help solve some of these problems. A politely worded note can be left on their door if you wish to avoid direct confrontation.
Some people have successfully used the "diversionary" tactic by planting catnip in another corner of the garden entirely, confining the destruction to one spot.
If you have not yet started your garden, put chicken wire down and plant between the wire. Cats dislike walking on the chicken wire and most plants (unless they grow too big) do just fine growing between the wire.
Other people have reported success with different sprays, gels, and products specifically formulated to keep animals out of your yard. Check your local pet store.
Lemon peels, soap slivers (use biodegradeable soap) dipped in cayenne pepper and other organic materials have also been reportedly successful.
Cats hate water: surprising them with a squirt gun (or turning your sprinklers on) can discourage specific cats from returning.
One person reported success in putting up cast-iron cut-out cats with marble eyes in strategic places in her yard. The decorative cats were apparently real enough to cats that they kept clear of her yard. Try looking around hardware stores or gardening stores for these. Lifesize cat statues might work as well.
If the cat actually follows your cat through the pet door, you might try an electronic pet door to keep it out (see Pet Doors).
To reduce the problem of birds on the ground (after dropped seeds) getting picked up by cats, use suet feeders instead of seed feeders.
You can try making an overhang on the top of the fence, if you cat cannot jump directly to the top of it. Use large bookshelf type angle brackets and drape netting or screening on it, to create an unstable barrier.
There are some "invisible fence" products for cats, where the perimiter of the yard is marked with a wire that will activate an electric collar on the the cat. Do not use these without supervision, and ideally they should be used in conjunction with a visible fence that the cat can use as a visual reminder of its constraints. This seems to work well with some cats and not at all with others.