Thank you for your answers .
2. no. That makes suppression a good counter to nasty hostile abilities
For completeness, i just found the reference to this in the rules (the "v3" rulebook PDF, pages 13-14):
5 - Attack Range and Attack Chart - Hostiles use the chart on their card to inflict various effects on your team.
Some Hostile cards have an effect, but no die roll or Attack chart. This text is only active if there is at least one Hostile Reticle that is not Suppressed and not Killed on the card.
6 – Special Ability - Some Hostile cards have Special Ability text at the bottom of their card. This text is only active if there is at least one Hostile Reticle that is not Suppressed and not Killed on the card.
Edit: as written, that means that "Screened by" also doesn't apply if the unit which is Screened By is fully suppressed. That seems kind of odd, but that's probably a very rare (or impossible?) corner case. i can't currently think of a condition where it would even be possible to exploit that, because of the timing of reinforcements and automatic removal of a suppression counter. Anyway...