For armour, I figure it works the same as in the XCOM videogame- armour increases health, so even 'bad' armour will still increase survivability. I'm not sure if that's actually how things work here, though.
Speaking of psionics, I wrote up an idea that might get around the range issue:
Psimine: We are continually beset by XCOM operatives, who we are forced to concede are incredibly talented soldiers, equipped by remarkably ingenious engineers. Our forces regularly find themselves outgunned by the Earthlings and their primitive but effective weapons. One area where our superiority is unmatched, however, is psionics. Yet we are under-utilising this advantage, using only relatively simple intelligence-gathering and ally-boosting abilities. It is high time we upgraded our arsenal.
What are a psion's weaknesses? Well, getting shot is a major one. So avoiding that would be great. Unfortunately, most psi-abilities require line of sight, meaning a risk of getting shot is inherent. Not so with the psimine, an ability capable of crippling foes without having to lay eyes on them.
A Gift-user imbues an object with psionic energy, then leaves it somewhere enemies are likely to stumble across it. When they do, the interference of their own psionic field destabilises the pent up energy, resulting in a burst of randomised psionic waves, which depending on strength (of both the psimine and the target's mental defences) will cause anything from a headache, through major confusion/panic, up to total psionic overload resulting in serious intracranial damage (in turn rendering the target unconscious, comatose, or even dead if they are especially weak).
A user may create a number of psimines at once, determined by their psionic potential (as each active mine creates a small drain on psionic energy). Any object may be turned into a psimine- rocks, corpses, doors, etc. Tying the psimine to an object this way makes it harder to detect (should XCOM ever develop psions of their own), and allows for makeshift 'psi-grenades'.
We have tested psimines on our psionic prisoner in order to maximise the damage they cause- using the unusually strong feedback they provide to tweak the creation method so that even a standard Sectoid is capable of creating psimines that can easily cripple an untrained human.