Crystals I believe are very rare, however it will also drop nobs and they are rare, but can seem to get one every unload or 2, obiviously will still take a bit to get enough to use, unless buying speakers!
Last I tested, it was a 0.026% chance to get a random xtal drop. That's roughly 1 xtal in 4000 quests chance.
Don't worry about xtal drops from quests. The drop rate is so low at ~0.026% that you are probably better off going inactive for a few days and returning to claim xtals. Instead farm for nobs which have ~0.95% drop rate and you can use those to regen and purchase stuff. Edit Ata should drop Stacy
I didnt know %, but did realize crystal drops are very rare, just was letting jackie know they would have a little better chance at collecting nobs and by my experience, it seemed to drop one nob every couple unloads. Its not something I would do all the time but if wanting to use for speakers or something like a regen, name change, etc... especially if running ebs with alot of spy only action, it maybe worthwhile.
After doing 80k+ quests I can say that nobility drops are 1 in 60 (used to be 1 in 50), and crystal drops are 1 in 7000.
Quest have always had poor drop rates after the quest has been completed. I can't remember the last time i hit a quest. In the market place there are free offers. But they take some time and sometimes the marketing people need ss of the fact you have completed said offer.
Doesn't matter which, but best to do the first one as it means least losses, plus it's at the top of the list so saves time. As for your other question, I think you are okay to hit a few at a time and not full unloads only. Although bear in mind you are best using the top % of your troop bar on an eb and the remaining leftover % on quests as this will give you best gold income.
To be honest I think it might be more time efficient walking around on the sidewalk trying to find coins and buying xtals with those than it is doing quests lol.