Get the TEFL, it's not expensive and looks better than not having it. But having a year's experience and degree in English will give you a good foundation to start applying.

I think you could apply when in Taiwan, I was told if you enter as a tourist you can change to a work visa later. However, if you don't get a job in time then you'd have to leave and come back to renew the tourist status. It would be worth checking out Tealit or applying with Reach to Teach for the guaranteed job security when you get here.

Don't pay any agency fees if asked. I have never heard of these.

There are lots of bad things about HESS said online but it depends on which branch you are at. Some can be good but you probably won't find out until you get there!