Those are somewhat loaded questions and some more information would be useful.
First since you are mentioning installing bigger tires I'm going to take a guess and say your Ranger is 4 wheel drive, and if so it will already have 4.10 gears and a manual transmission (I think that's the only way to get a 4 cylinder 4x4...).
Finding an Explorer 8.8 with 4.10 gears isn't too hard in junk yards, they're apparently most common in the '96 up 2 wheel drive versions I think which also have disc brakes, but that isn't the most common of ratios...
As far as installing the axle, it's fairly simple, either get the F150 flip kit meant to lower F150's which will get the leaf springs on top of the Explorer axle (they're meant to put the leaf springs below the F150 axle) and get new U bolts or get some weld on spring perches, then make some shock mounts out of steel strap or cut the mounts off of your old axle since the Explorer shock mounts are on the U bolt plates and won't work with the Ranger shock locations.
As far as is this swap needed and if your engine will handle it, the answer is not really and yes

. I ran a 4.10 geared 7.5" axle for a fair amount of time with my Ranger back when it was on 31" tires and even with the turbo engine and the only time I broke anything it was when I was pulling over a garage in first gear low range and the rope broke lurching things forward, and it just broke a spider gear which is a cheap and easy fix. The engine won't really notice a difference, but anything over 31" tires and you will be wishing you had lower gears which weren't even offered from the factory. There are lower gear options available but that takes some special setup to do.