PIE *dom- 'household'

PIE *dom- 'household' (e.g. Latin domus) is a noun-root whose genitive form *dem-s- is attested in the compound *dem-s-pot- 'master of the house' (e.g. Greek despótēs). Many Indo-Europeanists (e.g. Mallory-Adams) consider it to be derivated from *dem(h2)- 'to build', a root only attested in Greek (e.g. démō 'to build',  dómos, dõ:ma 'house') and Germanic (e.g. English timber). 

A part of the problem is that, unlike French, English doesn't make a clear distinction between the concepts of 'house' as a building (French maison) and 'household' as a dwelling place (French demeure). This explains why the French linguists Émile Beneviste¹ and Pierre Chantraine² think that PIE *dom- refers to the latter rather than the former.

IMHO, this suggests the original meaning was 'to remain, to live', thus linking it with Proto-Afrasian *dam- 'to live, to last, to sit', which AFAIK has no Eurasiatic correspondences.

In terms of linguistic archaeology, this points to the Neolithic, when (pre-)IE-speaking hunterer-gatherers learned farming techniques and thus became sedentary. By contrast, Afrasian speakers (mostly nomadic pastoralists) had a different lifestyle and didn't develop the household institution.
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¹ Le vocabulaire des institutions indo-européenes, vol. I, pp. 293-307.
² Dictionnaire étymologique de la langue grecque, pp. 292-293.

Latin pariēs 'wall'

Although some Indo-Europanists link it to Proto-Germanic *spar(r)e:n, *sparrio:n 'stake, beam', Latin pariēs 'wall' has no inherited PIE etymology. But IMHO it can be considered as a substrate loanword from PIE *Hwer- 'to close, to cover' (usually with various suffixes), a root from which I'd also derive Romance barra 'bar, barrier' and *berruculu- (Spanish berrojo, Gascon berrolh) 'a wooden or iron bar or bolt placed across gates on the inside'¹.

This would be a PIE B root corresponding to Proto-Altaic *t`jù:ru 'to hold, to obstruct' and PIE A *twerH- 'to keep, to hold, to fence', found in Balto-Slavic and also the source of Latin obtūrō 'to block, to stop up' and Romance *at-tūrō 'to stop'. 
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¹ Which Coromines thinks it was an alteration (possibly by contamination with ferrum 'iron') of Latin verūculum, diminutive form of verūs 'roasting spit' < PIE *g^wer(H)-u-.