Hey there, you may be interested in these questions I've answered before on Stalingrad:

If the Germans were better trained.....why did they lose at Stalingrad? As well as this question.

Were the Russians holding the entire river?

The entire front ran from Lake Lagoda to the Black Sea, so yes indeed they were holding the entire river.

Couldnt Hitler flank the Russians to the north or south

To the North would bring the Germans too close to the bulk of Russian reserves, and far away from the original and true objective of Case Blue: The Caucasus oilfields. This would be a dilution of purpose and strength.

To the South: The Germans were moving South, but not over the Volga, but rather along it. Their purpose was to use the Volga as a screen to cover an exposed flank as they drove towards Grozny. By the time hostilities were commencing on the perimeter of Stalingrad in September, the German forces driving South simply lacked the strength to break in. Prior to Stalingrad becoming an objective, the Germans split the Army Group committed to Case Blue into two sub-groups. This dangerously de-railed the focus of the operation and in effect served to do nothing more but dilute the power behind the German attack - one which was launched with no effective reserves to begin with.

Was this a propaganda war?

Some Historians like to forward that it certainly became one as the 6th Army got sucked into fighting in Stalingrad, but this is usually a purely subjective stance with only anecdotal evidence going in either direction. For whatever reason, the Germans decided to make an issue out of a city that was originally only meant to be contained and bombed as the main thrust of Case Blue shifted south.

The escalation of importance placed on Stalingrad doomed the drive South to Grozny to be conducted with insufficient strength as a result.

So to answer:

Why was Stalingrad important in WWII?

Stalingrad is important because it became so, I know that's an odd thing to say, but it became important because the Germans decided to make an issue of it - rather, force the issue. Their subsequent handling of the battle allowed for a wildly successful Russian counterattack which greatly shifted the initiative and deeply damaged the German's fighting ability, perhaps even irreversibly so.

Thanks for the answers.