Bigger Batches fermentation/lager times

I am starting to make recipes for 10 gal batches and I was wondering;
Will fermenting take longer then a 5 gal batch with the same gravity since there is more wort even though.

Also the rule of thumb for lagering, week per plato or a week per 10points Gravity. Would this change for a bigger batch with the same gravity?

On the ferment times: as long as you're pitching an adequate amount of yeast (ie, don't just pitch a single packet/vial/smackpack of yeast into 10 gallons of wort), it should take no longer to ferment 10 gallons than it would 5.

Heck, the pros ferment hundreds of barrels quicker than most of us ferment 5 gallons.

For the lagering, I know I've read the rule of thumb, but can't remember it. I typically lager anything for at least a month in my fridge, and haven't been disappointed yet.