Can Laser Eye Surgery Treat Astigmatism?

Yes, depending on how severe.
The most common side effect of laser eye surgery is dry eye; the laser often damages the nerves in the eye that stimulate the tear ducts to keep the eye lubricated. Sometimes this improves over a year or two, sometimes it doesn’t.
The next most common causes rings of light around lights at night. This can be distracting while driving, for example. This used to be more common but has gotten less so as technique has improved.
Next would be damage or infection; this is most often caused by improper care afterwards: not using the medicated eye drops properly, not wearing the protective goggles, rubbing or otherwise mistreating your eyes while still healing, etc.
Rare side effects include worse vision afterwards.
Not everyone is a good candidate for surgery: better pre-screening is one of the reasons that the side effect rates have been dropping. Talk to your eye doctor for more information and to see if you would be a good fit.
Some contacts you can sleep in for a short time, say, up to a week. Most eye doctors don’t recommend them, though, since contacts do, well, suffocate your eyes, and wear on the surface; wearing contacts too long — and this can vary person to person — can cause the blood vessels in your eye to overgrow into your field of vision. This worsens your eyesight and cannot be corrected; all you can do is never wear contacts and hope the blood vessels shrink back to normal (can take a couple years, if it happens at all). So, most doctors recommend daily wear contacts that you take out at night, to allow your eye to recover.