Yes, it will. But it doesn't stop drugs, prostitution and other such things in any way at all.
No , it won't it will just decrease them. When people are better off crime tends to decline.
Yes, crime is lower in countries with people who are better off. The problem is you're not making them that much better off.
Switzerland has a low crime rate because it has a high GDP. You're not making a higher level of GDP, the GDP will stay the same.
Now, what happens to people who decide they no longer need to work any more because they'll get a minimum income whether they get up in the morning or not? Well, it will mean that places that currently employ people who earn lower than this wage will have to pay more. So they pay more for their workers, they're going to have to charge more for their products. They charge more for their products then food prices increase, which means that those people who earn more will be less well off. And then they'll start demanding a pay rise. So then the minimum amount that is being paid to the low paid workers suddenly isn't enough to let them live because the food prices have just increased, and everyone else is earning more than them again and you're back where you started.
What would be better would be to make people good workers. Give them skills to do a job. Give them opportunities to do that job. Encourage them to work. The best way to encourage people to work is to not hand out free cash to them.