Can drugs affect mental health or the actions of people

Yes! I worked for a drug rehab in a non-clinical capacity. Despite that, I can state that based on my conversations with former and recovering addicts, that some needed treatment alone while others needed treatment and incarceration combined. I'm talking hard-core users here, with hard-core crimes to match. Some were truly frightening individuals who wound up in prison. Some died as a consequence of their addiction. Some went on to make full recoveries.

Can drugs affect...? Yes.
Should drugs be banned? Depends on the drug and how severely it affects those things, and I'm not an expert on this topic.

They absolutely can and do. Either directly or indirectly. I don't believe all drugs should be banned but many, if not most, should be HEAVILY regulated. This includes prescription drugs. Many on the market should not be as easily accessible as they are.