try adding some tension to the cable–>
look at the barrel adjuster and undo it (lefty-loosey), keep your finger on the cable so you can feel if its tightens or slackens.
deore is fine with deore shifters.
Difference between deore shadow and slx is nothing really, a couple holes drilled saves about 10g! but otheriwse identical.
The shadow deore is just the newer version of deore, looks different and is slightly better tucked away to avoid collision with things.
She may be right though, if you lean your bike up on its rear mech with no wheel in you may bend the hanger which in turn means that mech allignment will be off- usually characterised by it shifting fine in the middle but having issues at either end of the cassette (in some cases shifting off the cassette entirely, so make sure it cant do this)
Also it may be worth checking the higher (“H”) limit screw, to ensure that when the cable is not attached the cogs on the mech line up with the smallest ring on the cassette. If this is correct to begin with it makes setting up gears a whole lot easier.