Hi haeeey,
I think it should be alright to ask your teacher for a reference, even if it has been some time since they were teaching you. If you picked them as your reference chances are you had established a student-teacher relationship which they can also recall, regardless of years passed. I was in a similar situation when starting my university course and needed a reference from one of my previous teachers with whom I used to have a good relationship. They were more than happy to give me a reference, even though it had been a few years since they were teaching me.
Just ask them whether they would be happy to give you one, I am almost certain they would not refuse; a good teacher is pleased to see their students - current or former - to succeed and to be able to contribute to their success. Just make sure you give them enough notice though; this way they will have plenty of time to give due attention to your reference by the required deadline.
In terms of the different institutions, I would personally think putting either institution (where they have been teaching you or their current school) should be fine as long as you explain this/make a note about your former teacher currently working in a different school to where they have been teaching you. Your best bet is, however, to ask the institution you are applying to for clarification in this matter as they may be more strict/specific on exactly what needs to go on their form; I am sure they will be more than happy to guide you and you reaching out will also show them you are conscientious about your application.
I hope this helps, and please don't hesitate to ask should you have any more questions, and I will try to answer to the best of my ability!
Best wishes,
Viki
Student Ambassador
Recent graduate in BSc (Hons) Psychology and Sociology
University of Suffolk.