Yeppers!!! "Quote" adds the person's post to yours, just so there's no mistaking what you're replying to. You can also go in and edit out what is "quoted" (I removed the photos from yours) to help focus on, for instance, one particular section/comment/thought in a long post.
"Report" is to bring a post to the admin's attention, for instance if you think the post contains links to spam or virus-infected websites, or is completely off-topic or offensive or overly aggressive. If someone posts a bunch of nude photos with links to Russian porn sites while calling everyone on the board Nazi's, yeah, that should probably get reported.
Don't worry about English...you be you! Yours isn't the worst I've seen on a forum (including some who are American citizens and grew up speaking the language). As someone once said, "English isn't really a language by itself...it's more of the illegitimate offspring of a drunken party between a dozen other languages, some of which may or may not be dead languages, and nobody's really sure if any of it was consentual."