Yep, unless that unit's datasheet (codex entry) says otherwise.
For your example of Grot -> Aberration; Each Grot starts with Gnarlskin, CCW, and Flesh Gauntlet. One of your options is to purchase the Aberration upgrade for a single Grot. That stacks with the other gear (unless you swap it out with weapons of torture of course) .
I do believe yes you're correct that the Aberration could pick up a Liquefier since it does say "any" model.
As for the wracks, yes you can still take the liquifier/ossefactor since it says "for every five models in the unit". As for the Acothyst taking a Liquifier, 'course you can. Acothyst is allowed to take/swap upgrades from the Weapons of Torture and Tools of Torment lists, and the LG is on that list.
I dedicate these deaths to Odin Allfather, Spearshaker, One Eye.
Fleet Shadowmaker - Kabal of the Dying Sun; Cult of Marrow Excised; Coven of Lambent Hunger
Sons of the Last Breath - Chaos Space Marines
Host of Shattered Purity - Chaos Daemons