For the most part flights are run on a constant schedule; daily, every other day, weekly, etc. For example, [Delta flight 1529](https://www.google.com/search?q=dl+1529&oq=DL+1529&aqs=chrome.0.0l3.4103j0j4&sourceid=chrome&ie=UTF-8) is a non-stop flight from New York to LA every morning. I assume the same flight crew does a flight back from LA to New York every day as well.
As for the gates I’m not sure who assigns them but I seriously doubt it’s random. They need to maximize the traffic in and out, accommodate for delays, etc, they’re probably pretty flexible about which flights go where.
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