It depends on the font used, but 8 letters of the Latin alphabet have parallel lines:
B D E F H M N Z
With some fonts, you can add R and I
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0 because the letter t does not have anything to be parallel with but it is intersecting.
It really depends on how you write the letters. I count nine if there're all uppercase, but that's my handwriting.
A square has 2 pairs of opposite parallel lines.
Four. F, G, J, L
There cannot be parallel lines in any [plane] triangles.