“Can eye makeup cause problems to my vision?”

Wearing make up can irritate and dry eyes. To minimize burning sensation you can use artificial tears.

Yes

Using eye makeup can damage the glands along your eyelashes called meibomian glands. Damage to these glands can cause your eyes to dry out and your vision to become worse in the short and long run.
It is best to try to use eye makeup products that do not have the following compounds:
Sodium laureth sulfate or sodium laurel ether sulfate
Parabens: end in paraben like methylparaben, propylparaben, etc.
Benzalkonium chloride (BAK)
Benzyl alcohol
Phenoxyethanol
Formaldehydes:
DMDM-hydantoin
Quaternium-15
Imidazolidinyl urea
Diazolidinyl urea
2-bromo-2-nitropropane-1,3-diol.
Eyeliner wax
Waterproof makeup
Retinol or Vitamin A such as retin-A, typically acne creams
Botox in a jar (Acetyl-hexapeptide 3, marketed as Argireline)
Additionally, using artificial tear products can help prevent your eyes from drying out.

As long as you change out your mascara regularly like every 6 weeks, throw it out and replace it, and use good eye makeup remover daily, you should be fine.

Perhaps if you use contaminated cosmetics, risking infection.

As long as you clean up your make up every night, it should not harm your eye. You may wash your eyelashes and eyelid with baby shampoo once in a while.