A man went to a shop and they had a shovel.

Yes, you have to do some quests first. I think it was around mid or late Act 2 when he got usable as a member. I am not sure which quest, likely the questline regarding the sick man in the Last Light Inn / little boy and his ghost.

I got a quest log message that Halsin had left, though he was still in the camp and was usable in the party. Everything worked as if nothing happened.

Could be a bug.