I get the chords and can play several. My question is, does the Pro (paid) version of this site show strumming patterns?

I can know a song inside out, but still can't find the strumming patterns.

IF the pro version shows the strumming patterns I'll gladly pay the fee but not for just more chords and tabs which are useless to me without knowing how to strum them....
Some do. It depends on whether or not the author has bothered to put them in. Tab Pro is essentially an online version of Guitar Pro and if you have both Tab Pro membership and the Guitar Pro program, 9 times out of 10 you will find the guitar pro file that is identical to the tab pro tab. Tbh, I really didn't mind paying the £20 because I looked at it as supporting one of my favourite websites, getting no adverts and getting the other little perks, Tab Pro being one of them. At the time I purchased my membership I didn't have Guitar Pro which is £50 so it is really worth it.
It's tabs. Same function as guitar pro. Strumming patterns are generally something you'll have to "read" in tab format or figure out while you learn it; most tabs won't show what are down/upstrokes and never something like DDUUD and so on but it should generally be obvious from the tab, as you can hear the sound and slow it down, etc. Most tabs won't have chord names in them either, if you get the ad from viewing a chord/lyrics submission, it'll be misleading.
Get TuxGuitar (free) and download some tabs, because Tab Pro will display them in the same way so that way you'll understand better what sort of service it is.