Yes, bomb threats should be regarded as acts of terror. The purpose of such threats is to invoke fear and disrupt civil society, and should be treated accordingly. It is the same reason pranksters pulling the fire alarm get fined; it is a situation where authorities have to take the threat seriously.
The Danish man that threatened to blow himself up outside an asylum center was perpetrating an act of terror. Irregardless of whether or not the man is affiliated with a known terrorists organization, his actions were still intended to cause terror. Therefore, lone wolf attacks like this should be classified as attempted terrorists attacks.
No, I don't think that this was an act of terror, because terrorists don't threat to blow themselves and/or other people up, they just do it. This is more likely to be some sort of "cry for help" of a desperate man. He fled the war thorn country hoping to find better life, but ended up in the Asylum center instead.
Anytime people hear of a bomb attack or bomb threat, they instantly think it is a terrorist attack. If the person making the bomb threat is Middle-Eastern, it is difficult to convince people otherwise. But, many people use the threat of a bomb simply because they know how fearful everyone is of explosions. Not all bomb threats are acts of terror.