Yes, zucchini will develop a long stem and lean over. You can gently prop or tie it up so it doesn't pull the pot over, or just let it hang if there's no danger of it breaking.
The fruit that is yellowing has more than likely not been pollinated. Baby zukes will form, but if they are not pollinated by insects or you, they will shrivel and drop off. There are a lot of threads on hand pollinating squash. I use a small paint brush and apply pollen from the male flower to the female...it only needs a small amount. The best time to do it is in the morning as the flowers don't stay open very long.
My zukes will keep producing until frost or powdery mildew gets them. I'd say you still have plenty of season left in your zone. HTH