Minecraft – FTB Tesseract spits items back

You need to keep all chunks that are actively being quarried loaded or Bad Things^tm will happen. As for piping, nothing bad should happen if you don't keep all your piping loaded, however keep in mind that things won't move through unloaded pipes either so you won't get your materials till you go near the pipeline.

No, there's no limit to how many items can be in a chunk, nor in a pipe. I've piped a rotary macerator at full speed into a cobblestone pipe, and it handles them fine. The limitations of pipes are designed entirely around transport speed, not contents capacity. Minecraft's limitations on items aren't designed into the game mechanics — rather, too many items will simply overload memory and slow your server to a crawl.

Since you have a long pipeline, you are likely having parts of it unload when there are no players around that section. When this happens, the items can drop out of the last section of loaded pipes since they aren't "connected" to anything. You're probably seeing this more with all the quarries running simply because more items mean more chances to have part of a pipe that should be receiving items be unloaded at any given time. The easiest way to get around this is to make sure the chunks that have pipes running through them are always loaded by using World Anchors, Anchor Carts, or another block that designates a chunk to stay loaded even with no players around.

(As an alternative to buildcraft pipes you could also use RedPower2 pneumatic tubes. These won't transport items through unloaded chunks, but they have a more favourable failure mode: when a pipe can't deliver, items just rebound and get "backed up" in the tubes until there's somewhere for them to go. This would lower your throughput compared to a proper Anchor solution though, and would require rebuilding your item transport system over the entire long distance.)