Can I only eat it in Ayutthaya?
No. It is a dish eaten in other cities too. In Ayutthaya, it makes a good meal to pick between sights at the ruins.
Kuai Tiao Ruea · ก๋วยเตี๋ยวเรือ
If you want a bowl of noodles while touring the ruins in Ayutthaya, try boat noodles. Noodles and meat are served in broth, and along with grilled river prawns it is one of the best-known dishes in Ayutthaya. Choose the noodles and meat on the menu, then enjoy it with the broth while it is hot. They are eaten in other cities too, but it is a good meal to pick on a trip to Ayutthaya.

You enjoy the broth, noodles and meat together. The taste of the broth can change with the meat and the seasonings. Try it first without adding any seasoning, then add chili or other seasonings a little at a time.
Order after looking at the noodle type, the meat and the bowl size.
On a food trip in Ayutthaya, you can try boat noodles, grilled river prawns and roti sai mai together. A day that has noodles for lunch and roti sai mai as a snack sounds good. Still, boat noodles are not something you can only eat in Ayutthaya.
No. It is a dish eaten in other cities too. In Ayutthaya, it makes a good meal to pick between sights at the ruins.
No. The meat, offal, seasonings and broth differ by menu item. If there is something you avoid, ask whether it is used in the broth too, instead of just asking to leave out the meat.
If you want to read more about the food and the regions behind it, these sources are a good place to start. Ingredients and recipes can vary from one restaurant to the next.
Sharing image credit: Flickr user Alpha · CC BY-SA 2.0