The Mission mods that I played were mods that premiered at Origins. Specifically SRM 06-06 Fallen Angels, also known as SRM 06-06 Lose Permanent Edge. These are also mods created well after Street Grimore became legal and are checked and playtested by the CDT before becoming official.
Well timing doesn't really matter. Possession does not give Immunity to Natural Weapons in SR5. It could be an error, or a concious design - mission designers, just like any GM, can give their spirits whatever they want, including Immunity to Normal Weapons. But that's not as a result of being a Possession spirit and, unless your GM houserules it, player spirits don't get it.
If you take the Possession power as written, it actually makes Possession Spirits (including Shedim) fairly weak in comparison to normal spirits as their method of appearing on the material requires a vessel. And to take over a living vessel, it requires a contested roll. And while they do not need a contested roll for the summoner (which is awesome for Psionic Task Spirits), in terms of combat it takes the PC off the board until the spirit completes its task or is dropped. In terms of prepared vessels outside of the PC summoner, it takes a fairly long time to prepare a vessel, especially vehicles or drones that have 15+ resistance dice.
Mmm true, I guess, but it has it's perks as well. Possession itself - which for decent-force spirits has a good chance of success - will take out one of your opponents out of the gate, unlike Materialization spirits which have to wait for a full pass before they can do anything, if they start from the astral. Plus, the roll is about the same as any other spirit power, with about the same chances at success (and there's no reason why the spirit can't try again). There's circumstances where it's a big disadvantage, of course - but there's circumstances where it's an advantage as well.
And while you lose ItNW, you usually do have a higher body, plus the regular armor of whatever you're possessing - which is usually in the same order of magnitude (of course, not hardened, which is bad - but then, it works against magic attacks as well).