Botellon: just drinking and socializing outside, usually something a group of underage kids/young people would do. Not a party, not simply getting drunk. Like hanging out but with some alcohol.

Estrenar: to use/wear something brand new for the very first time. Sometimes when you are estrenando white shoes your classmates in school would try to step on them so they no longer look new.

The old-school English word for aprovechar was "thrift" or being thrifty. These days I hear it used mostly in the specific sense of saving cash. I don't often hear it much anymore in terms of conserving resources, but that is where it came from, and if you use it in that sense people will understand you.

As for sobremesa, that's not something I've enjoyed enough for it to have its own word, unfortunately.

Second one is "appreciate" in English.