Does a lack of faith lead to increased suicide and crime?

Correlation does not indicate causation. The other problem is that suicide is not a well defined and well reported data point.

If you look at the data by nation, it varies pretty wildly and suggests any number of factors that influence suicide. One painful point about connecting it with religion is that the converse is more or less to accuse the deceased of having insufficient faith. That's been a common Catholic theme, and having been to two funerals for men who took their own lives, I can affirm that it was painful watching the priests talk around that.

Me; not going there, in part because of those cases. The first funeral was for a 47 year old man whose marriage had blown apart (he could do pretty much everything but love his wife in a way she understood, it seemed--seemed like adjustment disorder giving way to depression), and the second was for a 22 year old man who was about to graduate college with honors and go on to grad school, and who had had something of a spiritual awakening, anxiety, and depression. I also suspect that a lot of the ~100k drug overdoses we have in our country may be in fact quiet suicides.

A very interesting outlier is that it's said that African-Americans have a much lower suicide rate than do whites. They have plenty of despair, plenty of difficulty, plenty of mental illness (though some expressions are lower), but especially for older blacks, suicide is much lower. Unfortunately young blacks are "catching up" in this dismal statistic.

Long and short of it is that you've got mental illness, trauma, darkness, and a number of other factors in there, and we ought to avoid a monovariant (one factor) explanation of a complex problem.

Truscott argues that the decline in religion can be tied to a loss of self-control and correlates that with more suicides and assaults.

This is really a stretch, especially regarding suicide. Suicide is rarely the result of a lack of self-control. In fact, in many cases it is due to influences that are beyond an individual's control. We are only recently beginning to understand more about depression and anxiety and what is happening in the brain when a person is suffering from these things. And while religion/spirituality can be a help to these people, it's a mistake to assume that memorizing Scripture or just having faith is the cure.

Truscott draws on data tracking crime on college campus and religious affiliation surveys to show that states with higher percentages of so-called “nones” — people who claim no religious affiliation in surveys — have higher rates of sexual assault on campus as well as higher suicide rates overall.

I'd be really skeptical of this as well. While I assume (and hope) that those with religious affiliations would have lower rates of sexual assault, there is also the distinct possibility that religious schools and churches cover up assaults rather than reporting them, skewing the numbers downward. This has happened with both the evangelical church and the Catholic church for a long time.