They’re not directly correlated, but generally, when you see lengthy contrails behind an aircraft, it’s probably cruising at altitude. Again, not directly related – it’s an atmospheric phenomenon[0] – but visible contrails are a safe indicator an aircraft is at or near cruise and are quite common. (Their absence, on the other hand, is not necessarily a counterindication.) And yes, an aircraft will pretty much always be visible to the naked eye, even up to 45-50k where some business jets live now. You may have to squint, but your eyes are pretty good at finding fast motion against a static background.

[0]: https://en.m.wikipedia.org/wiki/Contrail

Flightradar24

Contrails will help you find the jet, but you should be able to see it on a clear day.

Good question. I've seen passenger jets get pretty small to the eye sometimes, and they don't tend to go higher than 37,000 feet.

Alternatively, if you've ever flown across the country, mid-flight, look down.

The flight I took from the US back to Europe was at 42000 feet. Not that the difference in altitude matters much.