1) you might as well not give any money to anybody, because relatively no ones wealth will change
Blatantly untrue -- under basic income poor people will see their relative purchasing power increase, and rich people will see theirs decrease.
3) you will end up with inflation, because free money will create more demand, which in turn will result in smaller supply (relatively to demand) and higher prices
Or maybe supply will go up? You know we have an unemployment problem, right? More demand is exactly what America wants right now. It creates business and employment opportunities.
in the end these $1,000 after a couple of months will buy you only $500 worth of goods (end game is that these $1,000 will be worthless after some period)
Obviously basic income would be pegged to GDP, hence pegged to inflation. This is a non-argument.