Are police allowed to enforce laws of other states?

Basically, no. However, there is the possibility of agreements between states where each agrees to extradite prisoners. In those situations, someone picked up in one state can be held until the other state arranges transport so that a trial can be held.

No, as instrumentalities of state law enforcement, police can generally only act within their state, and for city police, generally within their city. One state's police entering another state to enforce its laws would be an infraction on that state's sovereignty.

well it depends like suppose you ran a red light while in DC but you didn't pull over

until you cross the line he can still cite you fo your offense since it was commited in DC

also it depends on what you did,,

also the metro transit police have authority in DC, Maryland and Virgina

a cop from one state does not have jurisdiction in another state unless he is invited by that states police department.