Does the lack of a 'may' mean that i HAVE to heal shuma of 1, even if I don't want to? (there are definitely occasions where I don't want to, namely when I am beginning the turn on click 2 against characters with damage reducers.)

I seem to recall something about giving characters actions always being optional, but I am not sure if this applies to this too.

There is no optionality presented here, so yes you have to.

You have to and if you read the power it's not an action at all.

You are never forced to give a character an action. If his power had said "At the beginning of the turn, give Shuma Gorath a free action to heal 1 click", then you would have had a choice. Alternatively, if they added "may" you would have had a choice. This has no choice. It is non-optional. It simply occurs.