Given enough time, will enough light from distant stars reach Earth so that our night sky will be more than 50% stars?
Nope! The universe's expansion is accelerating, which means there's a "horizon" beyond which light can never reach us, no matter how long it travels. Although the light always travels at the speed of light, the "amount of space" between photon and us can increase faster than the speed of light. This isn't a real "speed" - it's not any one object moving faster than the speed of light, it's all of space between us and the photon locally expanding a little bit - but it means the photon will never reach us. The acceleration means that this horizon will eventually shrink, as the expansion speeds up.
This means there's a finite amount of stuff that we can ever reach, and that can ever reach us. So you won't build up more and more distant stars & galaxies in the night sky forever.
There is absolutely no way to know right now what will happen. It's my personal belief that we aren't just expanding into nothingness forever, but will have endless interactions with other universes in the mesh of existence, or maybe we will stop expanding and collapse again. We may even know that answer in our lifetime. That said, the night sky could have just about anything in store, but earth probably won't survive long enough to see much of the changes.