Can I only eat it in Ayutthaya?
No. It is a dish eaten in other cities too. In Ayutthaya, it is a good choice for a meal between sights.
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 the dish is famous in Ayutthaya along with grilled river prawns. Choose your noodles and meat from the menu and enjoy them with the broth while it is hot. It is eaten in other cities too, but it is a good meal to choose on an Ayutthaya trip.

It is a dish where you enjoy broth, noodles and meat together. The taste of the broth can change with the meat and the seasoning. Try it first without adding anything, then add chili or other seasonings a little at a time.
Order after you check the type of noodle, the meat and the bowl size.
On a food trip in Ayutthaya you can meet boat noodles, grilled river prawns and roti sai mai together. A day with noodles for lunch and roti sai mai as a snack would be nice. Still, boat noodles are not something you can eat only in Ayutthaya.
No. It is a dish eaten in other cities too. In Ayutthaya, it is a good choice for a meal between sights.
No. The meat, offal, seasonings and broth differ by menu. If there is an ingredient you avoid, ask whether the broth uses it, rather than just asking for the meat to be left out.
If you want to read more about the food and the regions behind it, these sources are a good next step. Ingredients and cooking methods can differ from one place to the next.
Sharing image credit: Flickr user Alpha · CC BY-SA 2.0