Congrats for getting a new bike and your tri goals!
Alright - in regards to pedaling, you want the pedal to be on the ball of your feet.. it sounds like yours aren't... if you had a cleat, you' be putting the cleat at about the ball of your foot. There was a discussion yesterday or the day before about clipless pedals or clips or cages or power grips or bmx pedals.
It does sound like your sadle is too low - you shouldn't be able to reach the ground when you're in your seat... Basically when you're sitting in your saddle, when you extend your leg so that the pedal is at the bottom of the stroke... you basically want your leg straight with a slight bend to it. If you don't have that, your saddle's too low.
Last question... what gear should you be in? That sort of depends on your fitness. You probably already know this - but up front, the bigger the chain ring, the harder it is to pedal and the smaller ones make it easier... On a hill, you want to be on the small chain rings up front. In the back, it's opposite - the bigger the cog on the cassette, the easier it is to pedal and vice versa.
You don't have want to be pedaling slowly and pushing down hard on your pedals - that's just going to hurt your knees. You want to have a higher cadence in a gear that's comfortable for you... On a flat you probably want to be on one of the bigger chainrings up front & smaller on the back... But do what you can do for now, as you bike more and get in shape, you'll start hanging out in higher gears.