How important is it for the left hand to be nearest the mouth when playing tin whistle?

No. It won't change the sound at all. Most of the instructions will focus on holes being covered or open so use the fingers that make the most sense to you.

1. Why do you have to play the recorder with your left hand?
2. Do tin whistles have a hole at the back?

Why do you have to play the recorder with your left hand?

The reason for this is that although people are not made with left or right handed advantages in respect to recorder playing, the instruments are. Furthermore, all other wind instruments are made to be played with the right hand at the bottom.

Do tin whistles have a hole at the back?

Tin whistle players usually do not tongue most notes. ... A common method of achieving vibrato is to finger a note, and then quickly flick a finger on and off, not the hole below the fingered note, but the hole two below the fingered note, leaving an open hole in between.