Can I get braces even though I have broken molar tooth with cavities? (Photo)

You have missing molar. molar is very important tooth because of it will act as a anchorage. so as you have missing molar so TAD may require in your case. also you have cavities, so you have to get it filled before starting braces treatment. by seeing your photo, you have compromised oral health, so its my advice to go for invisalign instead of braces to prevent chances of cavity during treatment.

Yes, most times it's possible to do braces in such situations and manage the space well.
However, one would need to examine clinically to say for sure in your particular case.