Scaling strokes in Illustrator
Scale drawings in Illustrator, maintain proportions of line weights and effects
When you minimize large vectors that contain outlines & text to a small vector the stroke & size does adapt to the new size.
Is there a way to overcome this, or fix the final result? Also when I make the vector smaller and try to manually fix stroke I am giving 1 pt, is it optimal to go under 1 pt.?
Title mentions Photoshop, but you tagged it with Illustrator. I edited the title since your screen shots are clearly Illustrator.
In Illustrator, check the Preferences. Preferences > General > Scale Strokes & Effect. If that option is not checked, then strokes and effect retain their original size when you scale objects.
Oh, to answer the stroke size question.... yes you can go below 1pt. I would never go below 0.25pt however. Anything below 0.25pt runs the risk of being dropped when printed.