Both of the cranksets you mention are square taper. That's pretty standard and you shouldn't need to change the bottom backet.
To actually do the change you'll need a crank puller and a large hex/allen key (often around 8mm). It can be quite tough to pull the old ones off, even with the right tools. Don't even try and hammer them off, you'll just mash everything up.
If the square tapers are corroded underneath the cranks then to get a decent fit you might have to change the bottom bracket too. The problem here is that you wont know until you've pulled the old ones off.
When you're putting the new ones on, you'll find they go on easily, but getting them on straight can take some time.
There's some debate, I believe, about whether or not to grease the tapers when you're installing the new cranks, I didn't last time I did this. You'll want to get the bolt threads good and slimy though.
The derailer should be fine, 4 teeth wont change the size dramatically. If you can find the model number you should be able to find something that tells you the maximum size it'll comfortably take.
One last idea, if you're comfortable with just the 48 and there's no hills in sight, you could ditch the other 2 rings, front derailer, shiter etc. and save some weight.
From the rather blurry photo on the suntour site your current crank doesn't look like it'll rebuild easily, but there are plenty of suitable single cranksets available.