"Watch out for" can be used to give advice about threats at some point in the future. Things you want to avoid or be aware of because of potential danger.
E.g Watch out for the rabid dogs on your hike tomorrow.
"Look out for" can be used in a similar way to "Watch out for" but in my experience it's more commonly used for more immediate or certain threats and sometimes as an encouragement to be vigilant in a more positive sense (like you said "try to find" smth.).
E.g "Look out for that tree!" said Bob as his friend drove dangerously close to a tree.
"Look out for any clues along the way, they will help you solve the mystery"
"Keep an eye out" can be used to give advice about something that would be advantageous to be aware of. This might be used for opportunities or threats.
E.g "Keep an eye out for any special deals at the market, they have some real bargains."
"Keep an eye out for any bears, they might look cuddly but they'll rip you to shreds!"
In other words I would use "Watch out for" for possible dangers, "Look out for" for (almost) certain dangers (or sometimes points of interest), and "Keep an eye out for" for things of potential interest (or things which should be given significant attention) regardless of whether they're dangerous or not.