I'm brand new to ML, how many grains would a .50 cal self cast round ball be? And how many grains of BP would you recommend in a CVA mountain stalker?

I would check on the manufacturers website. There they may have recommended loads or an owners manual you could download and that would have load recommendations.

Since this is a roundball shooter, I am assuming either a flint or a perc gun? If that is the case a starting point would be 80 grains of 2F Goex and probably no more than 110-120 grains of 2F. But I am not familiar with that particular gun, so that is really only a rough guess. Your best bet is to check the manufacturers website.

That is a Traditional with a 1-48 twist.
Ball weight is 180 gr load with a 1-48 twist would be 50% of ball weight on an average that would be 90 gr with 20% + as a max and -20% as a starting point.
Check your owners manual for MAX LOAD a lot of CVA and guns have sever limits for max load and are dangerous if that is exceeded.

When I cast them out of pure lead, the .490 come out between 177 and 180 grain in weight. Since you have an older Mountain Stalker, try 70 grains, a .015-.018 patch, a good lube (if you have none, steal a little olive oil out of the kitchen and rub a patch lightly with that), and then one of them cast ball. I think it will shoot real well for you.

For target shooting 50grs is plenty, for whitetails 70-90grs will do the job...Sight in about 2 inches high at 50 yards and you should be dead on at 75 and within 2 inches low at 100 yards...

Cayugad, can it shoot miniballs too?

There is a mold made by Lee that produces a 360 grain .500 minnie ball. I have the mold actually. The thing I found is while the minnie is easy to load, and fun to shoot, it just did not have the consistent accuracy I demand from a hunting round. If you want to shoot a conical, try some powerbelts in the 245 or 295 range, or some maxiball. They normally shoot well in a 1-48 twist. Also there are some slip fit conicals that in some rifles do real well. All you can do it try.

I think I'll stick with round ball, though I may target shoot minnie just for fun. Can you recommend a website where one can get a single ball mold for relatively cheap? Would I need a .49 ball (i've read that). And, I know I'm asking a whole lot of questions, but where is a good place to get lead?

My dentist gives me lead, the X-ray block they put between your teeth and cheek have lead in them...I'd start with a box of store bought .490 balls before buying a mold...That way you know what size mold to use...

And before I forget, welcome to muzzleloading! It is a lot of fun!