In addition to all the above, you can also 'settle a bill / invoice'. This just means to pay the outstanding balance. If you're in a restaurant and someone asks you to 'settle up', they mean please pay! Also it can be a verb meaning 'to gently move into a new position''. e.g. 'The sand settled to the bottom of the glass.' or 'The oil settled on top of the water.' A settlement can mean either a small village or a legal agreement / payment that ends a dispute. So many meanings!

Settle down means to calm down. A teacher can say it to their students if the students are loud. Literally, "settle down" also means to put something down. For example, I bought a new lamp and I want to settle it down in the corner of the room. Hope this helps!

as well as the meanings Ava has listed above, there is "to settle" meaning to migrate and start living in a place- ie. to colonise. E.g: Europeans settled on the American continent, first on the east coast, then further inland. From this comes the noun "settler"- a person who goes to live in a new place, especially a place not well known to the settler's original culture

It has many meanings depending on the context. We are looking for a place for our family to settle down. - Means: We are looking for a place for our family to live for a long period of time, usually until the kids grow up. Okay everyone, it's time to settle down. - You'd say this if you were addressing a group of children and you want them to stop talking and find a place to sit down. Settle down! - Kids are probably jumping around and you want them to be calm, usually also quieter. Let's all get settled. - Usually would refer to finding a place to get comfortable such as a seat, but could be the floor depending on the context. Main idea is get comfortable because you will be sitting there for some length of time. This might be said before someone starts a discussion or if I were to read my children a book. There's also other meanings, like to "settle for" something means it's not what you wanted but it's satisfactory. After scanning the room, her eyes settled on the large table. - She stopped looking around the room and paused to look for a period of time at one thing. An object can be settled, but I think most of the time another word would suffice better, unless you were trying to illustrate that the object was "comfortably nestled" on a surface or around other objects. So yeah there are many ways to use this word!