Haigh! So this 'bridging t' as you put it actually seems to be the remnant of an old *tu-suffix

I’ll explain:
(a)caointeach is more straightforward so I'll start there - it is an adjective in
-(e)ach (< PCelt.
-*ākos, whence also ir.
-óg as a borrowing from Brittonic, notice Goidelic lenition of /k/ > /x/ vs Brittonic /k/ > /g/) derived from the noun
(a)caoineadh (the a- form is a further derivative btw) - note the ending in
-(e)adh, as is the case with many other Irish verbal nouns e.g.
mol > moladh, codail > codladh, cinn > cinneadh. You might notice that synchronically in Modern Irish, these VNs don't fall under any of the 5 declensions, as they're genitive formation doesn't fit with any of the usual patterns:
caoineadh ~ (gen)
caointe, moladh ~ molta, codladh ~ codlata, cinneadh ~ cinnte (note, however, fir1
cinnidh when used as the substantive "decision" and not VN "determination, deciding").
Now, words in this -(e)adh ending go back to Old Irish
-ed/-ad (where the lenited d /ð/ isn't orthographically represented), and are part of the u-stem declension;
caoineadh < caíned, moladh < molad, codladh < cotlud. This <d> /ð/ sound is the voiced equivalent of voiceless <th> /θ/, and <th> is voiced in word initial or final position beside an unstressed vowel by the 8th/9th century going into Classical Old Irish. So /-að/ < /-aθ/, e.g.
molad < *molath etc. This /θ/ is the lenited form that arose from the inherited /t/ in intervocalic position (among a few others) during the second lenition, around the 500 AD. This happened before the apocope of final vowels (for the dental to actually be in intervocalic, and not just postvocalic, position!), and from the (vowel) colouring found in
cotlud, among others, we know the final fowel must have been
*u. Therefore, these Oir. -ad/-ed/-ud examples are the descendents of a PC
*-tu- suffix which derived action nouns (i.e. verbal nouns) from verb stems, hence being tu-stems and in the more macro sense, u-stems. The vowels before the suffix vary since they reflect the vowels of the verb stems, so we have variants such as
*-atus, *-ātus, *-etus, *-ītus etc.
Going back to an example earlier to illustrate this, the verbal stem from which ModIr.
mol ultimately comes from ā-stem PC
*molā-, and therefore to build the VN, the suffix *-tu- was added, whence nominative
*molātus > molad > moladh. The PC genitive was supposedly
*molātows, however the syncopation of ā then occured whereby the dental /t/ came into contact with the /l/, which prevented its lenition (as the environment was no longer intervocalic) – so very roughly gen.
*molātows > *mol†tōs > *molto/molta > molta, and not OldIr.
**moltho > Mod.
**moltha with lenited dental.
This Proto-Celtic *-tu-suffix, by the way, comes from PIE
*-tus, which also gave us Germanic
*-þuz (> Eng. blas
t, draugh
t, yeas
t, lus
t, wais
t, threa
d etc.) and Latin
-tus (pul
sus, exi
tus, ac
tus, hia
tus etc.) among many others. It's everywhere

So that much should help explain that t in acaointeach.
Now, the t in
fuilteach is just a tad less clear. The most likely and straightforward answer is that Old Irish developed a late dental declension in
fuiled (see
http://dil.ie/search?q=fuiled&search_in=headword ) from the i-stem
fuil “blood” (< PC
*woli- < IE
*wolh₃-i-, i-stem o-grade derivative of
*√welh₃ “to strike, wound”). From this the o/ā-adjective
fuiltech (> Mod. fuilteach) is easily derivable. We don’t have a modern
**fuileadh ~ **fuilte, however – Scots Gaelic
fuil(l)eadh ~ fuil(l)idh “increase, profit, gain” is from OldIr.
fuilled “filling up; increase” <
fo-lína “fill up, supply”, a completely different thing altogether.
The adjective form
fuileach < fuilech without the dental is far more common in the older language, however, which just makes matters more complicated. A very unlikely, while not technically impossible, alternative is that this -t-form is the result of excrescence (addition of an epenthetic consonant), but I cannot think of any parallels.
I hope that much helps with the -t-.
On other points made, as has already been pointed out, none of these are compound words, just derivations through affixation (namely, suffixation).
When you mention ‘r’ as a linking sound, are you referring to the linking/intrusive r we see in some non-rhotic dialects of English? Linking-r would be “over all” with /ɹ/, and intrustive-r “I saw-r-a film” /ɹ/, where no r is historically there. If that’s the case, then no, Irish or Scottish don’t have this – we don’t have /ɹ/ anyway (unless you count more modern/urban/less proficient varieties today)!
Regarding PC
*dūno- meaning "hill" I am not convinced. Mod.
dún “fort; haven” < OIr.
dún o-neut. “fort, fortress; dwelling” < PC
*dūno-(m) “fort, rampart” < PIE
*dʰuHno- “enclosure”, a *no-derivative of
*√dʰewh₂- “to complete, come full circle”. Eng.
town < PGrm.
*tūną seemingly an old loan from Celtic, while Eng.
dune, down (i.e. hill) < OEng.
dūn < PGrm
*dūnǭ is possibly a late borrowing of PC
*dūnom.
I think its the English
down that is influencing this reading – Watership Down pops to mind! Despite what you will find on many websites, the meaning of [hill, high place] seems to be a Germanic semantic development while the Celtic words almost exclusively indicate a [secure place, fort, citadel], which do frequently appear on hills or in high places, however. Don't trust the web haha - most of these sites circle the same misinformation all the time, so etymologies or semantics found online must always be taken with a fist of salt.
The reconstruct
*liwo- is actually for “colour” (Oir, ModIr
lí, OW
liu > lliw), whereas the form
*līwo- (with long i) is the one you’re after, where we get Welsh
lli(f) “stream, flow” from. It comes from IE
*leyH- “flow” as a *wo-derivative.
Some food for thought anyway, a chara
