I'm not a MD but as a mental health professional and parent of an ADHD kid, here goes:
Yes, different medications are better than others for targeting inattentiveness vs. impulsiveness/hyperactivity. This is something a doctor would assess when choosing.
One of the non-stimulant medications (guanfacine) that we tried initially did cause anxiety and we discontinued it. The anxiety symptoms were gone within a day. We have not experienced with any other medication tried. Anxiety is also highly correlated with autism. You should find a good psychiatrist who can help you navigate side effects of meds vs. features of autism.
Some studies are finding that some kids who start stimulants early enough do not necessarily need ADHD medications as adults as it literally helps structure their brain to function more like a normal/non-ADHD brain over time. This really depends on the individual.
There are both extended release medications and short-acting medications. This depends on your child's metabolism. For example, my child has a fast metabolism and the long acting medications only actually work for about 5-6 hours. The short acting booster (ritalin) only lasts for 2.5-3 hours. But yes, they are out of their symptoms within a day. For my own child and my patients, I have not seen any physical or mental harm. But like all medical interventions, you weigh the benefit vs. the risk. In this case, the benefits tend to MASSIVELY outweigh the risks. There are decades of research on many of these medications at this point, which any good psychiatrist would be happy to discuss with you.
Good luck OP!