The $25000 can cover everything, I have a few friends that survive solely on the stipend while taking classes at Shida in Taipei. But you will definitely have to be careful with how your spend you money. You will have to share an apartment with other students, eat at cheap restaurants or cook at home. You can probably forget about stuff like going to nightclubs, and even meeting people at Starbucks is saved for special occasions. I think a more realistic budget is probably closer to 35000 a month.
As for the rest of your questions, as long as you show up for class you’ll get the money no strings attached. You dont have to show them how you are spending it and if your semester fee is higher than your stipend then you will just have to pay that out of your own pocket.
Also be aware of that it will take some time before you get your first stipend, we received ours 1.5 months after class started. So remember to come with enough money to live for at least two months, security deposit, semester fee++.