Even Jesus was tempted to do the wrong thing. The difference between sin and not sin is what you do with the temptation. If you have thoughts of suicide but don’t carry it out it means that you refused the temptation to sin (so no, thinking about suicide is not a mortal sin).
Self harm is a sin since we are supposed to take care of our bodies, but I’m not sure if it is venial or potentially mortal. Most people who self harm aren’t “all there” anyway so it would likely not meet all the conditions for mortal sin in many cases even if it was grave enough (which I’m not sure of).