If my phone is out if warranty by 2 weeks and it's a manufacturing problem will I still have to pay for a new phone?

yes. that's what no warranty means. you pay. unless apple decides to make an exception, in which case, you would need to ask them.

Probably. But, it certainly wouldn't hurt to ask very nicely when you take it to the Genius Bar.

Best of luck.

Yes, if it's out of warranty and there's a hardware problem, you will need to pay for replacement.

Regards.