First off, head over to the harvest forum. That's where all the knowledgeable canners hang out, and all your questions will be answered.

Second, pick up a copy of the Ball Blue Book, which not only provides recipes for many of the things you ask about, but also walks you through the canning processes.

Now, as to your first question. Those are all low-acid veggies. If you can them you have to either add acid (i.e., pickle them) or use a pressure canner. Otherwise it's not safe.

Peppers almost always turn out soft and/or mushy when home canned. You'd be better off drying those. Or you can freeze them; but then they're only good for cooking.

I don't know of any way you can make pickled eggs that do not require refrigeration. Yes, there are commercial versions. But they use different methods for commercal canning, many of which are not replicable at home.

Hope this helps.

This link is to the National Center for Home Food Preservation...it's my favorite reference. You'll find lots of info and good recipes here. There's a recipe for Pickled Mixed Vegetables...keep in mind you can swap the vegies as long as the proportions of vegies to pickling solution stay the same, and you can adjust seasonings to taste.

Here is a link that might be useful: Nat'l Center for Home Food Preservation