I always sort mine best I can. Get as much of the Zn and Fe stuff out of there so you don't have to worry so much about contaminating a good pot of lead. One stray Zn weight, melted down, will ruin an entire pot of previously excellent casting alloy.
When sorting, I keep a pair of pliers or side cutters handy. If there is question about a weight, I check it with the cutters. If it cuts easily, it is lead. If it takes considerable effort to even mark, you have Zn.
When melting your weights, keep the temp below 750 and you will avoid most issues with Zn. As stated, they will float on top of the heavier lead... IF they are not trapped below the surface.
As far as casting from the same pot as melting down the wheel weights, definitely do not do it if you are using a bottom pour pot. You are just begging for a leaky valve. You can flux your alloy til the cows come home and still get junk in the valve. Not so critical if using a dipper because of the lack of a valve to clog up.