Yes, the Lee Challenger will load handgun ammo.

Yes, carbide dies are well worth the money.

If you KNOW that you will never need the dies, brass, bullets for the .300 Win Mag, .243, and .270, then trade them off.
But if you decide later that you want them you may not get a good deal on them.

I strongly recommend you get the stainless steel case cleaning system, it costs more upfront but works better than any other.
Deprime the cases first and the entire case is cleaned.