So it's not about volume and PA-type technology. It's about clarity and even distribution throughout the room. Most soundfield systems that are available now have the option of a second microphone that you can pass round for classroom participation. This can work extremely well. It does obviously involve a slight change of teaching style in some cases, but many people who do use it find that it works very well. The children pass the mic round and they speak when they've got the microphone. If they do that you have then got an excellent system because you're going to hear the teacher nice and clearly but you're also going to hear questions and contributions from other children as well.
You can have as many infra-red systems as you like in a building. Because the infra-red doesn't go through walls, you're not going to interfere with the system in the room next door.