php - Htaccess rewriting multiple variables -

i dumb when comes .htaccess, through numerous attempts learn basics. here:

this current .htaccess:

rewriteengine on rewriterule ^$ /splash [l,r=301] rewritecond %{http_host} ^domain\.com$ [nc] rewriterule ^ http://www.%{http_host}%{request_uri} [r=301,l,ne] rewriterule ^([a-z0-9-]+)/?$ /index.php?cat=$1 [l,nc,qsa] 

i keep current functionality , add 2 things like:

• (keep) redirecting address without variable domain.com/splash
• (keep) redirecting of address without www address www (http://domain.com/xx http://www.domain.com/xx)
• (keep) make rewrite http://www.domain.com/aa http://www.domain.com/index.php?cat=aa
• (add) make rewrite http://www.domain.com/aa/bb http://www.domain.com/index.php?cat=aa&product=bb
• (add) remove trailing slash @ end if present

you can use:

rewriteengine on rewriterule ^$ /splash [l,r=301]  rewritecond %{http_host} ^domain\.com$ [nc] rewriterule ^ http://www.%{http_host}%{request_uri} [r=301,l,ne]  rewritecond %{request_filename} !-d rewritecond %{the_request} \s(.+?)/+[?\s] rewriterule ^(.+?)/$ /$1 [r=301,l]  rewriterule ^([a-z0-9-]+)/?$ /index.php?cat=$1 [l,nc,qsa]  rewriterule ^([a-z0-9-]+)/([a-z0-9-]+)/?$ /index.php?cat=$1&product=$2 [l,nc,qsa]