The pea vines sort of start dying from the bottom up. Mine usually keep going until the very hot part of summer gets here. The are full-on right now! But yes they will die on their own. You may need to decide which you want more. Peas, or corn. If you're just done with the peas for now, I'd pull em and get the corn going before it gets too late. Being in NJ, you're pretty close to too late already. Time to make a decision and commit!
As far as the garlic goes, generally speaking in my experience, the thicker the stalk, the bigger the clove. But not always. You may want to pull the huge one because the bulb is probably already divided and you don't want the individual cloves to start sprouting. I'd leave the other ones alone. I planted last Nov and mine aren't ready to pull yet. I have used a few, but they're not divided and a little smaller than golf balls in size.
P.S. you can always try to clear the dirt around that large garlic plant to see what you have before you rip all the roots and everything. That way if it's not divided you can just leave it alone.