I've lived in China for years.
TL;DR: This is not necessarily a date. It's good to attempt to pay for the bill (if given a chance), but I expect it's unlikely you'll succeed.
First of all, in Chinese/Taiwanese culture, would this be considered a date?
I'm not familiar with Taiwanese culture, but I expect it is very similar to China. In Chinese culture, there's several plausible non-date reasons that a Chinese woman would go to dinner with a European man:
In Chinese culture, asking someone out for dinner does not imply "date" like it does in Western culture. I made this mistake when a man asked me out to dinner, but it turned out he was married and he was assuming his wife would come too. He was just being friendly (and he cooked some amazing dumplings!).
She might consider you in a position of power or authority, and perhaps feel it's expected of her. I encounter this as a "teacher" in China: Chinese people will often feel obligated if I ask them to do something, as if they're unable to say "no". Chinese people (and I'm guessing Taiwanese people) consider "face" important; and maybe she fears that saying "no" would cause you to lose face.
She might want to practice English. This happens a lot in China, and it's quite frustrating. I don't know the specifics of your circumstances; you'll need to judge.
She may be one of those "Chinese culture is amazing! Let me show you" types. A lot of people here enjoy sharing Chinese culture with international people, and food is a big part of Chinese culture.
So while it's possible it's considered a date, it's also possible it's not considered a date.
If so, am I (the man) expected to pay for the dinner? (I would like it to be a date.)
Chinese culture includes "fighting over the bill". I recommend attempting to pay for dinner (if you get an opportunity; you might not), perhaps even gently pushing her out of the way if she attempts to pay. In my years in China, I've probably "won" this battle a handful of times.
If she lets you pay, I would interpret that as a medium-strength sign that it's a date. It's not a normal thing to let international guests pay.
If you end up splitting the bill, I would interpret that as a strong sign that it's not a date. This virtually never happens in China (I've done it with large groups, but even then they sometimes don't let me pay).
I expect she'll simply out-Chinese you at the cash register (or at the table via her phone), the cashier will probably ignore you and listen to her, and she'll end up paying via WeChat or Alipay. This happens to me a lot. I would not consider this sign either way, it's just part of Chinese culture and friendliness. There's other non-date-related factors which may encourage her to pay, like coupon apps (which are popular nowadays), and making things simpler for the wait staff.