I think the answer above is mostly right, but there is one important detail that can be misleading. I disagree that the investor would be indifferent between selling and holding if they have no views on the evolution of interest rates. They would be selling at a large discount to what they purchased (in our hypothetical rate spike scenario), likely incurring a loss far in excess of any received coupons up until that point.
It would be more accurate to say that they would be indifferent from buying that, now discounted bond (with a low, 3% coupon), and buying the new, par valued, 12% coupon bond.
In regards to your first question, you would hold until maturity, assuming no default risk (credit risk is different from interest rate risk), because presumably when you first purchased the bond you were satisfied with the stated yield to maturity, which you will still receive. If you sell, you are going to lose money.
For your second question, current yield is just coupon / price. So yes, it shot up because price dropped, but the coupon stayed constant. The important relationship here is yield and price, which are inversely related. Think of it this way: the bond you bought in this scenario pays 3%, and will until maturity. When you bought it, if market rates were 3%, it priced at 100 (par). Now, if market rates are 12%, a newly issued bond would have a 12% coupon to trade at par. This means a new buyer would only be willing to buy the 3% coupon paying bond at a discount big enough to cause the yield to maturity on that bond to be equal to the yield to maturity on the 12% coupon bond, which is a really big discount.