Not usually although in some circumstances you may need to (for example, labs in science/engineering degrees may require you to wear specific PPE for safety reasons which is impractical or impossible to wear with one or both items). For just like lectures or seminars, no. Although you probably might want to, as often lecture theatres and seminar rooms can get quite warm!
I don't think there is a rule relating to this at University. So it depends on whether your classrooms have heating or not. If it is cold, I think the lecturers would not mind if you had jackets or hats on.
no - if you need to cover yourself for cultural / religious reasons then you would be fine. For some sciences etc I imagine you might need to switch jacket for labcoat etc.
In general I believe most universities would not feel strongly on this as generally it is a quite relaxed environment at university and being in lectures compared to how you would of been treated in secondary school. Due to some universities being quite old buildings / being very big the rooms can feel cold on occasion and I will often sit with a jacket or a coat on especially during the colder seasons. A hat would be okay there are people in my lectures that wear hats but I feel like there is an unspoken rule in society that you don't wear hat indoors so it possible someone may ask if you would be comfortable taking it off but I think this would be quite extreme and unlikely as we don't know the circumstances of why you are wearing this and it could be personal. If you study a subject that requires you to wear Personal Protective Equipment (PPE) then you may have some restrictions on what is deemed appropriate or not as well as practicality but again if this makes you uncomfortable for what ever reason you can discuss this and inform your lecturer.
Hope this helps, Maddie, second year Health and well-being in society student at De Montfort University
Not particularly no. You have a lot more independence at uni and there's nothing you really can't wear etc. It's polite to take hats and jackets off when you're inside and staying somewhere but do you have to? No. Things are a lot more flexible when you get to university level, I've seen people come into lectures in tuxedos before haha.
Hope this helped! Lucy - Digital Student Ambassador SHU
Generally, university is quite a mature space where this is left up to you as an adult, unless for safety reasons. You should be able to do what is comfortable for you.
Normally you don't have to! Just dress in whatever you are comfortable in! Some courses may have specific requirements for dress codes in labs or if you're patient facing but uni is usually quite relaxed otherwise!