Do you have to assign another settler to food if you plant in another location but both are in the Sanctuary?

Is there a limit on how many planting one settler can tend to?

There is a limit. I think it's 6 or twelve depending on the crop. I could be wrong. For your first question, I am interested in knowing the answer as well

There is a limit. Easy to test. Plant 18 crops. Assign one settler to the farming. Wait a little and you will see how many food your settlement produces. Remember, 1 food = 2 crops, except mutfruit 1 food = 1 crop. Per settler it's 6 food. Here is the http://www.reddit.com/r/Fallout/comments/3v6cc5/assigning_settlers_to_crops/.

Cheers,

-Klevs

Each settler can produce six food. That is 12 plants that produce .5 food, or, six that produce 1. (or various iterations in between.)

If there are available settlers they default to farming, so if you plant food you will see the food counter go up unless you run out of free settlers. If you assign an existing farmer you will see the food counter go down as they clear the crops they were initially farming from their objectives, and then the food counter will go up as they add the new crops they are assigned to in their objectives. If a farmer hasn't got 6 units of food to farm yet, he will farm any other units (up to 6 units total) available in the same settlement.

One thing to bear in mind is that while unassigned settlers act as farmers, it is always better to assign them as farmers manually because I think once your settlement hits five unassigned settlers, even if they are farming, your recruitment beacons will no longer attract new settlers.