While chains can be had quite cheaply, it might be possible to resurrect the one you have through liberal application of a steel wire brush and the oil of your choice. Just make sure there are no frozen links.

Count the sprockets at the rear, that's your answer.

But this decides chain width, in one way or another, and will do nothing to sort out the issue with chain length, which you mention in the headline. Chains are generally sold a few links long, and will need to be trimmed to fit your particular bike setup. Get a chain breaker tool, and preferably not the cheapest versions. It'll make the job a lot easier.