Is it possible to upgrade Schwinn Willy to use an internal gear hub?
It is possible -- you can either find a 36 spoke internal gear hub (since you have a 36 hole rim) and have the wheel re-built with the new hub and bodge on the cables for the IGH shifting. Alternatively, there are automatic shifting hubs (e.g. the SRAM Automatix) which will also have a coaster brake and no shift cables. That being said, its probably going to be cheaper to get a new rear wheel than have someone building the wheel up with a new hub. 

But, in the end, on a 300 dollar bike, you're going to be better off economically just buying a new bike with gears.

As for the crankset, you can swap that out, but you'll still have only one gear ratio unless you add a front derailleur (which your frame likely doesn't have mounts for, so you'd have to bodge it on). You may also need a different bottom bracket in this case. As in the case of the new wheel, this isn't worth it economically.

Generally, though, swapping the rear cog on a single speed is a better choice. The Schwinn ships with a 19t rear cog. If you're willing to work a bit more on the hill, you can swap that out with a 16t or 14t or something. This is quite economical (probably 20 bucks for the cog and a bit for labor at your local bike shop). If you want to do anything to this bike, this is likely the only thing you can do that is economical. 

The end of it is: if the cog swap isn't favorable, get a new bike with gears.