Should I break office rules?

Really bad idea. It will be a mess if it breaks up. If you want to pursue a relationship, see if one of you can transfer so that you are not her boss.

Doesn't really sound like a good idea, if it's found out that you were trying to hide it, people will wonder why. If you date her openly no doubt others will gossip about what sorts of benefits she's getting from you...and if it ends badly, either way, how does THAT affect your work space? I also think it's good for couples to have separate jobs/spaces.

Be VERY careful. I've seen many employess including managers lose their job because of the eventual break-up that occurred. And there was plenty of gossip and whispers that spread through the office and I'm sure most of it was not even true. link.