It's pretty easy to live cheaply in Taipei if you need to. I can eat very well on NT250 per day if I want, without even trying. Say, 50 for soy milk and a 燒餅夾蛋餅 for breakfast. 80 buys me a nice 三寶飯 for lunch (at the place I'm thinking of, this is duck, sausage, and some other kind of meat that's really good but I haven't bothered to ask about
, plus vegetables and lots of rice). So then I have 120 left for dinner, which is enough for a good dinner, maybe teppanyaki at the place on Shi-Da road, for instance. I do usually spend a little more than this, but this sort of day isn't uncommon at all, and you could easily do cheaper. I have friends who eat in the student cafeteria nearly every day. Rice and soup are free there, and the other stuff is cheap, so you can eat a decent meal for NT50 or so.
Anyway, tutoring, part-time teaching, and proofreading have all been easy enough to come by. I've been offered three gigs just in the past week, actually. In my experience, most of this sort of work (including all three jobs I just mentioned) is found by word of mouth, so try to make friends with some people who do this. People will often contact them first, asking if they know anyone who could take the job.
For me, proofreading is more lucrative than the others, but that's because I've found somewhat of a niche, and have enthusiastic recommendations from previous (and recurrent) clients. I charge NT1000 per hour for individuals, and 1500 for the rare business that hires me. For tutoring I only charge 700 per hour, but it's more steady than proofreading. You have 2 years of experience on me (minus a couple of months) in teaching ESL, so you should be able to ask for more than 700 per hour for tutoring. In fact, I know non-native speakers who earn 700 per hour tutoring. If you're teaching a class you may have to go with what they offer you, though you may sometimes be able to negotiate.