1) how do you know someone talks about the room or the bread? 방 and 빵 sound like the same.
As you know, 방 and 빵 have different spelling and different sound even though both sound like the same to your ears.
Furthermore, we understand by the context or surrounding words even when both are confusing
빵 is not used with the verb 덥다
Here is similar question for
how do you know someone talks about the volt or the bolt? both sound like the same to native Korean's ears.
2) Why one is with subject particle 이 and one is with topic particle 은?
There are many so questions and answers about 은,는,이,가 here in italki.
In short for this sentence,
이 was used for unexpected, unusual, unfamiliar situation
은 was used for expected, usual, familiar situation
방이 덥습니다 is uncommon situation. (it has the nuance : The air of the room is not hot usually, but The air of the room is hot now)
빵은 뜨겁다 is common situation (it has the nuance : The bread is hot usually, and the bread is hot now)
3) Is 덥습니다 the polite form for 뜨겁다?
덥습니다 is polite form for 덥다
뜨겁습니다 is polite form for 뜨겁다
덥다 means "the air is hot"
뜨겁다 means "the object itself is hot"
빵이 덥다 (X)
방이 덥다 = 방의 온도가 뜨겁다 The air of the room is hot