Can I only eat them in Ayutthaya?
No. They are eaten in other cities too. In Ayutthaya you could pick them as a meal during a break from sightseeing the ruins.
Kuai Tiao Ruea · ก๋วยเตี๋ยวเรือ
If you fancy a bowl of noodles while exploring the ruins in Ayutthaya, try boat noodles. They are noodles and meat served in broth, and together with grilled river prawns they are famous in Ayutthaya. Choose the noodles and meat from the menu and enjoy them with the broth while hot. They are eaten in other cities too, but they make a good meal to pick on an Ayutthaya trip.

It is a dish where you enjoy the broth, noodles and meat together. The flavour of the broth can change with the meat and seasonings. Try it first without adding anything, then add chilli or other seasonings a little at a time.
Order by looking at the noodle type, the meat and the bowl size.
On a food trip to Ayutthaya you can meet boat noodles, grilled river prawns and roti sai mai together. A plan of noodles for lunch and roti sai mai as a snack would be a good one. Even so, boat noodles are not something you can eat only in Ayutthaya.
No. They are eaten in other cities too. In Ayutthaya you could pick them as a meal during a break from sightseeing the ruins.
No. Meat, offal, seasonings and broth differ from menu to menu. If there is something you avoid, rather than asking them to leave out the meat, ask whether the broth uses it too.
If you would like to read more about the food and the regions behind it, these sources are worth a look. Ingredients and cooking methods can vary from one cook to the next.
Sharing image credit: Flickr user Alpha · CC BY-SA 2.0