You have a good buddy!
1. You don't need to wash them but you can if you want to. Any dirt or trash will be lighter than the melted lead and will float to the top.
2. Wheelweights do contain tin. It should be enough to get good fill out. I would cast a few bullets and see before adding anything. Sawdust is good flux. It seems like Pine works best. Maybe the Rosin in it? I usually flux 2 or 3 times with sawdust and then 1 more time with wax. Old candles, gulf wax, crayons, ect.
Zinc weights will have a different appearance. Usually they will appear more shiny or more gray looking. And most of them will have either the word Zinc or a "Z" on them.
A goog habit to get into is to never add material to melted lead. It does not have to be cold, just not liquid. If moisture gets under the surface you can have a steam explosion and get to meet "The Tinsel Fairy"! I've melted wet weights before with no problem. I filled the pot before lighting the burner and the moisture cooked off before the weights melted. I've even melted sink or shower traps that had moisture in them.
A couple of comments: The weight that was soft may be a stick-on weight. All lead stick-on weights except for one type are soft and close to pure lead. Having a dedicated "smelting"pot and keeping raw scrap out of your casting pot is a good idea. Another good idea is looking on the Cast Boolits site and reading the stickies about wheelweights.
Your post is kind of timely! I just came in from the garage after sorting a bucket of weights that "mysteriously" showed up in my drive way! Did I mention "good buddy"?
Feel free to ask more questions. I enjoy scrounging for lead, sorting lead, melting lead, talking about lead, you get the picture!