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No, Because the lines in a triangle meet, so they cant be parallel because parallel lines never meet.
No it can't, because if a triangle has two parallel lines then it ceases to be a triangle and becomes quadrilateral or a polygon.
In two dimensions, lines can be parallel, angles cannot. So no plane shape has parallel angles.
Perpendicular lines meet at a right angle so a right angled triangle has two lines which are perpendicular to eachother. However there are no parallel lines in a right angled triangle, or any triangles for that matter.
A triangle, no matter the type, can never have any parallel sides. To try this out, draw any two parallel lines on a sheet of paper and try to make a triangle out of it.