Can I run to the store while my rice is cooking in the oven?

Absolutely.

I start dinner and then go pick up my daughter from school at least 3x per week, and that round-trip takes almost 1 hour.

Haven't burned the house down yet! :)

I have never ever ever heard of anyone cooking rice in an oven. How far is the store, from your house in Texas to the Grocers in Arizona?

Turn the stove off, leave, come back and turn the stove on again but I don't think salsa is going to help your rice that was cooked in an oven.

i usually lower the oven temp just a little bit just incase the store is packed when i get there and i power walk thought the store eventhough people look at me like im nuts i have money in my hand and if the change will only be a few cent i hand the cashier the money and keep it moving

there are many rice dishes cooked in the oven.

I do all the time.

Leaving the oven on is safe but if you are concerned, turn off the oven but do not remove the rice. When you get back, turn it back on.

I'd do it. It won't burn to a crisp while you're out for 30 minutes and cause a house fire. If it doesn't normally catch fire while you're at home, head to the store!