Is it possible to be happy and suicidal at the same time?

Yes, but it's more of a psychological disorder that can be treated with Cognitive Behavioral Therapy. Sometimes we psychologically link things together, such as sadness and suicide. When you feel sad, you feel suicidal because it makes you feel better. When you are depressed and suicidal, it is essential that you seek immediate treatment because without hope, you are a lot more inclined to do the deed. If you are happy and suicidal, you should seek treatment such as CBT because it really helps you understand how the mind works and what lies you tell yourself.