1. This happens all the time, the market is very efficient. If your idea has any merit there's almost always going to be a competitor near you.
But, as your business evolves, you'll move closer to some competitors and further from others. I think of it like ships sailing in the sea: you might be close to a competitor right now, but have very different trajectories (moving up vs. down on the pricing curve, expanding your product assortment horizontally versus vertically, focusing on different segments of the market, improving on different aspects of the product, etc).
2. One of your jobs is going to be to navigate that competitive landscape. It shouldn't necessarily keep you up at night, you need to focus on the problems in front of you instead of being constantly paranoid about competitors, but you do need to be strategic about where you steer your ship to stay differentiated.
Is the other product exactly the same? Could you differentiate on brand, focus on a different market niche, do it cheaper/better, have better design?
3. It depends on #2. If I could think of a way to differentiate and leap frog the first product, I would try that. If not, I'd probably launch it anyway if I've spent 6 months on it. What do you have to lose?
4. You can't avoid it altogether. There will always be competitors if you're creating something valuable, if not now then later. One of my friends runs a company that builds SaaS for janitorial quality control (a relatively niche market) and even he has competitors. Navigating the competitive landscape is just something you have to continuously do as a founder.