They can move to the coop, full time when they are around 6 weeks / fully feathered.
In terms of putting them outdoors - you can do this from a few days old, depending on the temperatures (and make sure that you are at home to keep an eye on them). If you do this during the warmest part of the day, for a short time, to begin with they should be fine. You can increase the duration of their "playtime" as days pass. It should be warm though, and certainly not raining.
This helps to acclimatise them to not having a heat source, exposes them to pathogens in the soil (that they will build up immunity to) as well as let them entertain themselves, pecking at grit, grass and little bugs.
Assuming your brood inside your house, then chicks can do without heat from around 10-14 days (for standard sized breeds) - assuming your room temperature is 75F or above. I brood my chicks in a room that averages around 75F and turn off the heat source after 10 days. From day 5 I turn off the heat source during the day, for increasing periods of time to wean them off the heat.
I'm sure other members will be along to share how they do things. There's no right or wrong way so whatever advice you receive I'd suggest doing what you feel is the best thing.