To answer your questions:

Will four BCs be good enough to perma tank the gate guns?

In terms of what amount of DPS you'll be needing to tank take a look-see here. Another thing you might consider is having a dedicated tackler to point any ships coming through the gate. You might miss out on many kills if your target is smaller and nimbler than your fleet and you have no means to pin them down.

I am also curious of where the ships should sit while on the gate

This really is down to personal preference and ship fitting. You hardly want a mini-fleet of enemy BCs popping up right next to your arty Drakes. Here is also a nice link to another similar question regarding distance from the gate.

Finally, what fittings are best for low sec gate camps?

I would once again suggest having a dedicated tackler with scrams and webs to pin your victims down. The rest of the ships should be fit for high DPS and a armor or shield tank that is able to comfortably take the sentry gun aggro.

Are reppers and rechargers needed with 4 BCs or will the guns cycle enough to share the damage?

Logistics is always nice. But not imperative for the kind of setup you're going for.

Also remember to scout the gate a bit before you set up your camp. This could also help with fittings as it should give you an idea of what will be popping through gates on a regular basis. Are you going to be seeing tons of indys or faction fitted battleships. What is the activity in the area like in general? The last thing you want is large fleets jumping on top of you while you're taking sentry gun damage. Oh and if you happen to be gatecamping a lowsec gate that goes into highsec, don't jump into highsec space by mistake until the GCC has taken its course unless you want to be Concordokken'd.

EDIT: Added another link for the optimal distance from the gate when gate-camping.