Panhandling is literally illegal, and I'm reasonably sure that anyone who's "homeless" gets picked up by the authorities and taken away somewhere. So it's hard to assess how common either is. That said, because the police are extremely effective at keeping out drugs, I don't think it's nearly as common as in America.
Regarding crime, Singapore is one of the safest in the world. A lot of that comes down to effective policing and extremely strict sentencing that puts criminals behind bars for a very long time.
Family ties are a lot stronger, so a lot of people falling on hard times do get substantial help from their family members. But there's minimal governmental safety net of the type you find in Western Europe.
Does that lead to a lot of homelessness and crime?