Lets say the song I want to sing, is just in E standard. I find it WAY easier to sing the song if I have the capo on 2nd or 3rd fret. I was told I'm a baritone/tenor. I just have difficulty reaching the low notes when tuned to standard. Is that normal?
Songs are in keys, not tunings. Recordings might be in a particularly tuning, but you can play any song in any key in any tuning for the most part, though some combinations are obviously easier or more typical.

Everyone has their own range, and so you should sing in whatever key best fits in your range. Tenors don't sing particularly low, with C3 being their typical lowest note for that classification. For some genres, songs don't go that low, but in others like country and bluegrass it is more common.

There are other options though, such as singing songs (whether in part or in whole) in a different octave but the same key or modifying the lowest notes to a higher chord tone. For example, House of the Rising Sun is done usually in A. Some people have trouble hitting the low E2 note at the end of the verse, so you can replace it with a G# to make it reachable. A lot of bluegrass tenors also tend to sing it up an octave, making the range E3-A4 rather than E2-A3.
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