Question about sheet music? (piano)?

Okay, so I started online piano lessons, everything is going great, but I'm a little confused on some things. First off, I learned that whenever there is a # symbol next to a note, then it is a sharp note, but the thing is, I've printed out tons of sheet music and I know what the songs sound like and so when I come to a note on the sheet music that's supposed to be sharped, it doesn't show that it's sharped? Does some sheet music just not put in the sharp symbol? If so, that's really annoying and can lead to confusion and can lead you to learn the song incorrectly if you have never heard the actual song that you're learning. My second question, is it absolutely necessary to learn all the chords? My lessons teach me chords and I have a book on chords. Are chords for just being able to read music easier as in looking at sheet music and being able to play it easier since you can identify the chords? Does NEED to learn chords to be able to just read sheet music? Can one learn how to play more advanced songs without memorizing all the chords on piano? Thanks.