Is this iPhone screen fixable at an Apple store?

The screen is certainly fixable/replaceable, but you might question whether it is cost effective in light of updating to a new phone or finding a good-condition used replacement. Screen replacements of the digitizer assembly assuming the underlying LCD is not damaged on older iPhones are approximately what a new-to-you used phone might cost at certain locations such as Mobile Madness chain stores. You best bet is to drop by your Apple store and get an estimate, and then do some comparison shopping.