I observe a galaxy that is 100 million light years away: what do I see?

If it's 100 million light years away, most likely it is redshifted. At only 100 million light years distance, it's not anywhere near the "horizon" which is about 14.5 thousand million light years away. You observe what the galaxy looked like 100 million years ago. 100 million years is not very long in terms of galactic evolution, so it probably pretty much looks the same "now" as it did "then." It's moved some in that amount of time, so it's shifted away a bit from where you're looking (not that it matters). Something in that galaxy "now" looking this way, if it had a powerful enough telescope, could see dinosaurs here on Earth.

You see the galaxy as it was 100 million years ago. It may be red or blue shifted depending on whether it is traveling away or toward us. I don't know about the cosmological horizon - I suppose this could be farther away than the "edge" of the universe. But the universe is somewhere around 15 billion years old, and 100 million is just a fraction of that number.

You would see the galaxy as it was 100 million years ago. The red/blue shift would depend on if it was moving toward or away from us. The universe is at LEAST 12 Billion years old but some scientists recently began to beleiive that it is trillions of years old, there is no "horizon" in space, you can see as far as your telescope will allow.