It is okay with most advertisers but check the program terms to make sure. As far as redirecting is concerned, it is okay though.
Sure, you will get the commission. There is no restriction on redirection stuff is imposed. Redirect wisely and improve your earnings.
As long as the customer clicks on the affiliate link, the cookie is placed you'll be fine on the affiliate program.
yes, as long as the cookie is set, it's fine but some advertisers are against so you will be safer just contacting the particular advertiser and ask if it's fine with them, if you mask the url.