Yes you can add the extract while its still cooler,its preferred it mixes better right after the mash,stir it good. You may want to strain your hops using a strainer when adding it to the fermenter,plus it helps aeratesyour wort some.Do you plan on shaking it or do you have another means of aerating your cooled wort?
Wait a second, i think your only steeping grains right. You are not using base malt? Just steeping grains? 30 min steeping grains is not a partial mash but if you have base grains this is a mash because you are converting starches from the base grains to sugar(what extract is). If you only have steeping grains(crystal malts,roasted malts and such),you are only basiclly getting flavor and color and not more fermentable wort.