So if/when I eventually switch to using a conical fermenter, I assume I wouldn't want to dump the entire trub/yeast cake at the bottom during fermentation. Do you typically wait until your "primary fermentation" period is over in the fermenter, and then dump all of the trub? If not, how much do you leave? How long do you wait before getting rid of some of the trub at the bottom? In most cases, would you completely avoid using a secondary and use the conical fermenter for the entire fermenting process?
Just like any fermentation process the best practice is to leave the beer on the yeast cake until it is completely done fermenting. And not just actively fermenting. Resting on the primary cake after terminal gravity has been reached for a few days goes a long way towards getting cleaner tasting beer.
I'd say do not dump until at least 10-14 days post pitching, assuming an appropriately sized pitch of healthy yeast was used.
typically i dump the trub just as the fermentation is winding down...about 4 days in. This cleans out all of the garbage. If I had a hard time removing trub before the conical, I will do a quick dump about 30 minutes after filling the conical. To avoid oxygen exposure during a dump, I attach a balloon to the conical using a stopper and a short piece of tube, connected to a john guest fitting (for a good seal). I let it inflate for about 10 minutes, then dump. as the pressure builds, the headspace gases compress, so a small amount of volume in the balloon is necessary. After I dumb the trub, I attach a homemade yeast harvester. It is a closed system that attaches to the bottom valve that allows beer to fill it. of course i purge it with CO2 first. periodically i agitate/swirl the conical and the beer inside of the harvester gets displaced by falling yeast (since you remembered to leave the valve open) and develops a beautiful settled yeast cake ready for storage. when i am ready to remove my beer, I close the bottom valve, remove the yeast harvester, and fill my keg as normal.
If you're brewing an ale, I don't think there's any disadvantage to dumping the whole trub. If you were planning to pitch another batch onto it just drain it into a sanitary container. The trub is just inactive yeast and proteins. You'll most likely still have yeast floating around, and draining the trub will probably stir some inactive yeast back up into the beer. I'm not sure whether the same holds true for lagers.
I think most people wait until primary fermentation is over, although I'm sure there are some people who wait till the end and people who do it every few days.
The main concern would probably be how much air are you willing to let in the fermenter? Every time you drain trub or take samples it sucks in air (or, if you forget about your airlock, airlock liquid, hopefully not water). If you purge with CO2 it doesn't really matter, but if you don't you could possibly get some oxidation (although definitely no more than transferring to a secondary would give you).
Instead of a opening a dump valve to drop the trub into a container full of air, why not Just leave the valve open and let the trub settle into the container? When you want to isolate the beer from the trub, you could just close the valve. Then you can unscrew the container and havest the yeast.