Betta fish not swimming

I acquired a betta about a week ago. He's in a little plastic aquarium - maybe half a gallon. The first couple days I had him he was pretty active; but for the last two days he's just been hanging out near the bottom of the tank. I put food in today and yesterday and he didn't come to eat any. The cheap thermometer I bought says the water is about 74 degrees F. I've never had a betta before and I don't know if this is normal behavior or if there's something wrong. He's a nice dark red color, and he doesn't look like he's in distress, but what do I know? Maybe the activity of the first couple days was a reaction to being moved and in a new place. You can't do much in a half gallon tank, I guess. Is this normal for these fish?

I have a couple other questions, too. I filled a gallon jug with tap water and used Betta Plus bowl conditioner in it; I've replaced about a third of the water out of the jug every 3 or 4 days. Bowl conditioner doesn't 'wear off' after sitting around in a jug of water for a week or so, does it?