Question
1) A King Henry fly trap

2) Once the heads fall off after one - two months, should I trim the stem or leave it be?

3) I've had the plant for going on a month. It lives outside, so it gets plenty of sun, and I water it every morning and change out the little bowl of water it sits in as well.

4) Portland, Oregon.

Answer
Hi Julia,

What you're calling a "head" is actually a leaf.  Keep in mind that Venus Flytraps are plants, and not like animals in any way.  The trap is a structure at the end of the leaf.

As leaves age they eventually begin to brown and die, just like they do on all plants.  When a leaf/trap starts to brown, just clip it off at the base.  King Henry Flytraps tend to be floppy, so that is very normal.  

Your care of your plant sounds very good.  Our general rule with sun for Venus Flytraps is wherever you have your flytrap, you should be able to grow a tomato plant in that spot.  If it's bright enough for a tomato, it's sunny enough for carnivorous plants.

Good Growing!

Jeff Dallas
Sarracenia Northwest
http://www.growcarnivorousplants.com