>Are Visual novels, galge, and dating sims the same things?
Visual novel = genre derived from adventure games where you basically only read text and select choices. More or less synonymous with "novel game".
Galge = This is in most cases used in opposition to "eroge". Both are games where the main focus (or one of them) is relationships with female characters, but galge doesn't have sexual content while eroge does. It's common for successful eroge to receive console ports, though, so you will see people referring to e.g. the original PC version of Key's Air as "eroge", but subsequent console ports and all-ages releases as "galge".
Dating sim = contains gameplay/raising elements, like stat-building and random events.
Keep in mind that it's difficult to draw clear lines because Westerners use these terms differently than the Japanese do, and because there is a lot of intersection.
>Or a visual novel that makes me feel like I'm important for the plot instead of giving me just 1 or 2 choices throughout the whole game.
You can look at this tag on vndb: https://vndb.org/g1025?fil=olang-ja.tagspoil-0.tag_inc-1025;m=0;o=d;s=rating
Alternatively you can try a dating sim like Amagami, or something with gameplay like Baldr Force.