Samsung LN37A450, PS3 and 1080p (?)

[Norris]

When I hit the little INFO button on the remote for my LN37A450, it supplies me with the entertainment mode I am in, but also at to the bottom of that information it says "1920x1080 24hz". It is saying that because I am using a PS3 to watch blu-rays and have the 1080p 24fps setting enabled, but here is my real question(s) :

1.) This TV is suppose/advertised as having 720p, but by through some slight of hand, am I actually getting 1080p?

2.) If not, then why does the TV supply that information?

3.) And double if not, and it is just converting it down to 1080i, does 1080i 24fps exist and that is what it is reading it as? I ask because it doesn't specify in that INFO box a "p" or an "i" after any of the settings, 720 or 1080.

4.) And secretly I fiddled my way into the service menu, which from what I remember says that the HDMI ports are 1080p......truth?

Sorry if this was all covered somewhere else on the board & I appreciate any help/answers that can be supplied.