You can add all of those things you listed and they'll all compost. The peach pits will still be recognizable for a long time, but other than those, everything sill compost pretty quickly. If you have a hot compost pile, you don't need to worry about seeds or any bacteria the potted plants may be bringing with them.

If the waste from the rabbit bin starts to smell, add more high carbon matter (sometimes called browns) such as wood pellets, sawdust, shredded paper.

Welcome Silvergirl: I'm not an expert but can answer a few questions for you.

I don't know anything about rabbits or what "wood pellets" you use for bedding. Is there anything in it besides wood? Wood is good if small. The waste is good to use, many people do with great success. In fact I think some people keep rabbits just to get the poop for their compost!

Any large object will take longer to rot. This is true of anything from bluejeans to fall leaves. Its better to chop up the fruit and veggie waste, mulch the leaves, and cut up cotton. A banana peel is slow, so chop it up. Hacked up pumpkins go faster than whole. Use a mulching leaf vacuum, or run a lawn mower over them. Whole leaves are slow to break down. In autumn gather, mulch, and store all the leaves you can, they're great composting material.

Hot composting will kill seeds and plant disease. (Is hot compost your goal? If so it might take a little experience until you get the hang of it). If a plant has obvious disease, I don't add it to my compost, I trash it. But you can't fear all bacteria since it is bacteria and fungi which make that wonderful compost. You can compost healthy looking plants. Again, cut them up into smaller pieces, even the roots or they might take forever to break down.

Also, add moisture as you build the pile or you will never get adequate moisture throughout the pile for composting.

Welcome to composting and to the forum. As you progress come back and ask questions. There are many knowledgeable people here who will help you. (Not me, I mean people who know more than me...)

Have fun! I love my compost and love to play with it.

Karen

If you hadn't lost your compost cherry, you could have composted it. :-)

A couple simple composting rules for newbies:

If it smells, add more browns (wood chips, shredded paper).

If it doesn't seem to be doing anything, add more greens (rabbit poo, kitchen waste, human urine).

Fruit, and any other food waste, stuff you can eat, can and should be composted. Some of the harder (pits) material may take a really long time to be digested.
Plants in pots, if they are not going to be saved can be composted and, diseased or not, should be composted. Nothing vegetative, stuff that once grew, should be just thrown away since it all adds to your soil.

Here is a link that might be useful: A really good composting tutorial