Okay - dripping pot - not good. Plants (most of them, rice is an exception) shouldn't sit in standing water. It's too much for them, plus you might find you've created a lovely mosquito habitat. So don't water until it drips; water until the top of the soil is moist, then stop. If the plants need water, you'll know it because you've see dry, brown, crackly leaves (usually. There are always exceptions, but that's more or less a rule of thumb to follow).
Bring them in before it hits freezing. If the weather report says there's going to be a frost, take the plants in, and leave them in until Spring, even if it's 30 degrees C the next day. We all know that autumn and winter can kind of come and go but the plant is going to get mighty cold if you leave it out too long. Better safe than sorry. We usually take ours in at about mid-October or so.
Dead leaves - brown or yellow - ah, it depends on the plant, of course. If the leaves readily come off, take them off; the plant's about to shed them anyway. If not, don't pull, don't force the issue. As for leaving them in the soil (I think the idea there is, bury the detached leaves in the soil), eh, it may or may not help. Of course you should check whatever is shed - if it's got scales or webbing or any other evidence of insect interest, don't bury it in the soil and instead throw it away so that it's far, far away from your plants, which may or may not be salvageable. For very bad insect infestations (I doubt that you have this, I'm just telling you this for the future), the remedy is to discard the plant and get another. Really. It's hard to get rid of the little buggers once they're established.
PS Is this your Bidens plant?
Is this the zilverblad?