Do I email Mattel about a broken figure???

Yes. A ton of people have sent them emails due to broken figures in the past and they have always been very helpful and usually send out another one!

I think every Regal's hand breaks. You literally CANNOT turn them.

That was actually one of the most infamous problems with that Regal figure. Mattel made the left hand to stiff or something and everyone who goes and turns it real hard as soon as they get it, it breaks. I still have yet to even try to turn mine because i have heard so many other ppl complain about theres breaking so i do not even want to try.
Just shoot Mattel an email and tell them what happened and send them the numbers on your box of the figure and they will give you a $12-$19 voucher for it depending on how much you tell them you paid for it.

I have 2 E8 Regal's and their hands are fine. Don't email them you call the cust ser number on the back of the card. They'll ask you a few questions and send you a manufacturer coupon for the cost. They won't send you a figure

You could, but you would have to drill a hole through the existing peg that broke. Then get a screw small enough to fit in the peg, but tight enough that it won't separate from the peg when you pull it out. Heat the area up with a hair dryer to soften the plastic when you pull out the screwed peg with pliers.

Even easier, just switch arms using the heat method.

Mattel figures just do this sometimes. I bought 3 DCUC Batman Beyond figures where the left legs did the same thing. I eventually learned that if a DCUC has problems with the legs moving to just split the pelvis, and sand down the area with the peg rests in the inner mold of the pelvis. It is a shame we have to do this with some of our figures, especially when they are nearly $20 each