unsure about the coin op self service type of wash.
no the tunnel washes do not mess up paint over time, however on darker paint jobs it does create swirl effect that eventually you would need to high speed buff.
there are some express tunnel/free vacuum car washes that do approx 10-15k cars per...
i would suggest to not put any money down
it will not make any difference to your interest rate.
only thing putting money down will do is allow the dealership to get a better rate from their bank to sell to you.
no need to tie up addition funds