You've got questions. We've got answers.
You don't want to over-wash your beard. Every time you wash it, you strip it of the natural oils that keep it healthy. Unless you work in a dirty environment, you only need to wash it once or twice a week. You should also make sure that you are using an all-natural soap or shampoo (no sulphates). Rinse it daily with cool water.
I recommend you do this daily. Especially during the dry, cold winter months. If you see that your beard is too oily, decrease the usage or the amount you are using. If you have a full beard that is longer than 1" (25mm), you should use about a dime to nickle size amount of oil, or a full thumb nail scoop of balm. Increase if needed for longer beards (3+ inches). Decrease for shorter beards and goatees. After you have it in your palm, rub your hands together and then work the oil into your beard, making sure you get it down to your skin. Use a brush to distribute the oils evenly.
Both have the same purpose, and basically the same ingredients. The big difference is, balm is made with butters and waxes that give it a thick consistency, allowing it to provide more weight and hold. Oil, on the other hand is basically a conditioner only.
Do not over do it here. Let me say that again... DO NOT OVER DO IT! You should only brush it once after applying your oil/balm in the morning, and maybe once at night. I recommend using our boar's bristle brush. Once or twice a day, you can use a comb to remove any dust or crumbs or small children that my have accumulated throughout the day.
Rubbing, brushing, stroking, etc. is counter productive to keeping a healthy beard. I know it's awesome, but try to leave it alone.
"I don't like it getting in my mouth!"... or "It's so messy when I'm eating". I've heard it all, and I've been through it. You just have to decide whether or not you want a longer mustache that you can style. If you do, you just have to push through the uncomfortable stage. Brush it to the side, and use balm/wax to hold it if you need to. After a while, it will be "trained" that way and you'll have an awesome mustache. Keep stock in napkins.
This is a normal thing for most men just starting out. Unfortunately, it is also one of the main reasons many men give up and shave. You're going to experience at least a little itch, but you're a man right? You can handle it. All of your whiskers have a sharp end on them from shaving. Those sharp ends are poking your skin, irritating it. Also, dead skin from your face is shedding and getting caught in your beard. Make sure you are rinsing your beard out every day with cool water. The beard oil/balm will help to keep your skin moisturized, and it will soften the whiskers. Make sure that you work it down to your skin when you are applying it, as well conditioned skin is just as important as well conditioned hair.