Healthy bettas always beg for food and act as if they are starving, even if they are stuffed! Normally, 3-4 pellets, twice a day, is a good average to go by. This is what I feed all of mine, and they all have a healthy size. The way you tell is, look down at him from above. If he has a nice smooth taper from behind the gills down to his tail, he's eating right. If it bulges slightly behind the gills, cut back a little, and if it sinks in in that area, up it a pellet per feeding.
You can also tell from the side, if his tummy is smooth with a slight roundness, he's good.
The second question kind of depends. If he's in a small tank, like a gallon, I'd be hesitant to leave him for a week, although since he isn't eating, he won't be making much waste. If you do leave him though, just an extra pellet or two, no more, per feeding would be OK, and make sure when you go there are no leftovers in his tank to foul the water, and give him a fresh water change. Depending how long the trip will be, and the possibility of the water being quite different where you're heading, I think maybe the best option will be letting him stay where he is.
You can also tell from the side, if his tummy is smooth with a slight roundness, he's good.
The second question kind of depends. If he's in a small tank, like a gallon, I'd be hesitant to leave him for a week, although since he isn't eating, he won't be making much waste. If you do leave him though, just an extra pellet or two, no more, per feeding would be OK, and make sure when you go there are no leftovers in his tank to foul the water, and give him a fresh water change. Depending how long the trip will be, and the possibility of the water being quite different where you're heading, I think maybe the best option will be letting him stay where he is.