Completely missed bidding on an item that went unsold -

[ksld]

Is it against the rules to contact the seller and ask if the item is still for sale, or if she is going to relist or whatever?

It'sagainst the rules to offer to buy it outside of eBay, but no harm in asking if they are going to relist it.

This is not an eBay site, I do it all the time ask someone if they have a bin price for an item they are selling.

If you want to be straight contact them and ask them if they will relist on a BIN so you can buy it, tell them how much you are willing to pay so they can list at that price.