As others have stated, this is not something you need to worry about if you're in Taipei. You will have to be careful as a pedestrian, cars and scooters don't give right of way to pedestrians.
Airbnb is present in Taiwan. You can check out their website or this FB group: https://www.facebook.com/groups/RentalApartments/
Not all the rentals on there will be long term. Lots of people coming here for 3-4 months to study Chinese and leave. There's lots of options near the schools that have mandarin learning programs in Taipei.
If you plan on studying, why not apply for a student visa? This will be helpful when finding a place to live and some small things here and there.
Your passport will be most important, make sure you don't forget that
It's your first time outside of Europe...or err..the UK, sorry.
So I understand your concern. If you don't want to share an apartment, you're looking at around 15,000NT to 30,000NT per month (not including utilities and management fee) for a studio with nice amenities and 24/7 security. Take note that not all studios have a full kitchen! They may not allow cooking too!