Chai-paani: tea and water. As slang, it means a bribe. The language course HindiPod101 lists it among the Hindi expressions used to ask for one.
Beeda uthana: to pick up the betel roll. It means to take on a difficult task. The Rekhta dictionary explains the custom behind it. When help was needed with a hard problem, a roll of betel leaf was set out, and the person who picked it up vowed to solve the problem.