Find:

Each time your Dot recognizes one of the items in the top section, they will be award 60 Dot Growth.  There is a cooldown period of 1 hour individually for each recognition task, which can be repeated a maximum of 20 times.

When you have completed a recognition task 20 times you will notice the icon get a yellow background - tap on it and you can claim 100 Keeper XP!

Foraging:

In the Foraging section are the surfaces on which you need to get your Dot to Forage, again your Dot will receive 60 Dot Growth for each successful Forage on each Surface.  Each Surface also has a 1 hour cooldown (as per the recognition tasks).

Once again, completing 20 Foraging tasks will allow you to claim 100 Keeper XP.

Summary:

The timer underneath the Task shows you the cooldown time before you can complete the Task again - currently, each Task has a 1 hour cooldown.

There is no time limit on these tasks, but once you have completed them all for a Dot, you can do no more with that particular Dot.  You can of course switch out to another Dot and do them all again if the Keeper XP is what you are after!

So, each Dot can gain up to 15600 Dot Growth from these tasks, and as a Keeper you can also claim up to 1300 Keeper XP from each Dot you complete the tasks with!

Dot Growth from these Tasks stacks with other Dot Growth from the usual Dot Desires.