They do not have a plane. They charter a 747 from China Airlines when so required.
There are 5 of those for your perusal. I also recommend you to read the pamphlets on why the Tiaoyutai are a sovereign part of the ROC.
Somewhat amusingly, Chiang Kai-shek's administration privately justified its nuclear weapons program (despite the ROC being a signatory to the Non-Proliferation Treaty) by noting that China (the other one, of course) was one of the nuclear-weapons states recognized by the NPT. Since the ROC was the legitimate government of all China, so the logic went, there was no problem with the ROC developing nukes.
Thinking Taiwan's view regarding the diplomatic allies pending crisis:
Yes it will be a disaster, who are these ally countries again and can anybody find them on a map? They just plan for this eventuality right now and switch promotion efforts, but the Ma admin people want Taiwan to be part of China so they won't care as long as they keep their pensions.
I don't know if it would make a huge difference, really. It makes Taiwan less legitimate in everyone's eyes, but I feel that the world's nations would take the same hands-off, finger-waving approach if China invaded Taiwan with 22 friends vs. China invading Taiwan with 0 friends.
Yes they do have one. A Boeing 737 800 exclusively for TW govt use. Operated by the ROCAF
Here she is :
Paraguay, Haiti, Guatemala, Honduras and co. invasion of China....Cute indeed..
Oh yes, how did we (society) manage to absorb the hundreds of toll takers that were let go? I kind of enjoyed handing my money to someone.