I use a moisturizer that contains SPF 50 on a daily basis, and mix a bit of foundation in there. Should I wear sunscreen separately?

Not necessarily. If the moisturizer's spf formula blocks both uva & uvb, you shouldn't need more sunblock. Further, the foundation may add a bit of physical sun blocking (like the zinc oxide people put on their nose at the beach). If the moisturizer blocks on one type of ultraviolet, then supplementing to cover the other type may be prudent if you're going to have significant sun exposure. Wearing hat helps, too.
Broad Sunscreen key. Your basic combination is ok on the surface however the key is not so much in the spf as it is the ingredients. A broad spectrum sunscreen is key to prevent photo aging. Look for sunscreen with either zinc oxide, titanium dioxide or avebenzone.