False.
Add, at least:
3. The attacker can refuse to mine on top of certain blocks
(Which prevents such blocks from ever being accepted into the longest chain.) The protocol allows that as well. I'm still not quite sure if this is a complete list.
But your 2. would only be correct if you did not include the phrase "to cause economic harm." The protocol is agnostic about why something is being done.
You are right it would probably make sense to differentiate between the rewards of a miner and a regular transaction.
What is a block? Effectively it is a set of transactions including the one where the miner pays himself. The block is linked to previous blocks and has a PoW (in the case of bitcoin)
Double spends can only happen if you "erase" a block by presenting a longer chain in which it is not present.
In a sense robbing a different miner of their rewards by intentionally making a new chain is very similar to a double spend.
[edit] I'm unsure if the selfish mining approach is as viable as it is claimed to be
You would obviously find a pattern if a pool consistently tries to maliciously remove blocks.
Of course it can't be prevented but at the same time you have a similar effect to that of double spending.
Everyone will know you are behaving badly and will shun you. Furthermore you are negatively affecting your profits (loss in confidence of the system).