Minecraft – How many chunks do I need to keep loaded to keep quarries working in Buildcraft

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.)

Yes, a quarry will keep chunks within its area of operation loaded before and after doing its thing. They will only be unloaded when the Quarry block is removed.

To test this, I simply set up a system that pumps items out of an Ender Chest (from the Ender Storage mod) into a regular chest near a quarry that had reached bedrock.

Then, I went to the Nether, restarted the server for good measure, and put items into the corresponding Ender Pouch. They started disappearing, which means that the chunks in the overworld were still loaded.