I'll take a stab at each one:
PB sandwich - OK as long as your pile doesn't have a lot of other fats (the PB might take a little longer to break down)
crackers - OK
pickle juice - OK though might be salty, and from what I understand salt is genearlly not a good soil/compost amendment
gutter sludge - depends. I wouldn't take the sludge from our gutters because some of it always contains little roof shingle particles and I really don't want that in my compost. but the leaves are great.

These are good questions.

First I cannot imagine leftover PB&J sandwiches but they can be composted, in small qauntities. Peanut butter is ver high fat which is difficult for the bacteria in your compost to digest. Small amounts of pickle juice may also be acceptable, depending on the size of your compost pile. A 4 x 4 x 4 pile will be able to take more than a 2 x 2 x 2 pile would, but keep in mind that pickle juice is a preservative.
The small amount of particles from your roof shingles should not be a problem either since they will be in your soil anyway. If you have enough to be concerned about it is time to look at replacing the roof.

Put it ALL in. What came out of the eavestrough is as you think it is, decomposed leaves. Its a great addition to your compost pile.
Peanut Butter. If you think peanut butter is not what should be put into a compost pile of rotting garbage, then throw it away. Better still though, give it to your neighbors who will throw it into their compost pile.

Don't be led down the garden path by scary stories of putting stuff in a compost pile that will harm it.
Meat, if its buried deep, fish carcases, if its buried deep, milk solids, if its buried deep will decompose down as much as anything else. It just depends on how much goes in there and if you bury it under a lot of grass clippings, other food waste, leaves and soil, you've done well by your pile.
All this food, don't let it go to waste.
It all has microbes -- and I haven't met a dangerous microbe yet I wouldn't let eat in my compost pile.

Patty,
Oh, you are going to love having compost! It is truly the gardener's black gold.
Go ahead and compost newspapers (shredded, and not the slick ads) and cardboard and food scraps and garden waste and definitely leaves. If you have rodents or loose dogs in the area, you might not want to compost meat scraps or dairy. It isn't that the meat and dairy are bad for the compost, but the dog/rodent digging into your pile is.
We have two compost piles going, the "add-to" pile and the "ready-to-use" pile. There is no such thing as having too much compost at hand.

I'm with jerrycan and marlingardner on this. I put everything into my compost bins. I do "lazy girl" composting--just pile stuff in until the bin is full, close the top and leave it alone while I start using the other bin. When the second one is full, the first one will have nice, rich compost.

My only problem is that the peanut shells never seem to break down. It keeps the compost nice and light, but the neighbors look askance. So I just blame the squirrels!
Ginny

The only reason not to put meat in the compost pile is because creatures will dig it out. If you have it boxed in or don't care if a raccoon makes away with free dinner, then go ahead and put it in.

There are more reasons to leave meat out of compost than racoons. Meat/dairy/fats are broken down differently and can promote dangerous bacteria growth. That bacteria won't die unless you keep your compost at a high temperature (150+ for multiple days). It is possible for some of this bacteria to be taken up by plants. High temperature composting or fermenting composting systems are required to safely compost meat/dairy and large amounts of fat.

Although there is very little point in reviving a 13 year old thread, one can safely compost anything that at one time was a carbon based life form. And that would include peanuts/peanut butter, other fats, pickle juice (sugar, vinegar, spices), meats, breads and dairy products. Just be cautious with the quantities involved.

And of course, the cleanings from your gutters.

I try to remember passerbys' sensibilities and compost accordingly.