Some belated comments (I was away for a while):

1. I don't think -rim has to become -lim after l since we have lr attested in balrog, talraph.
2. The cluster str doesn't necessarily change to thr, cf. mistrad, ostrad (the former is misread in Etym).
3. Where does the dual -id come from? As far as I'm aware, -id only appears in nœgid which may simply be a plural of noged 'petty dwarf' or a sideform (cf. diminutive  _-eg/ig_ in atheg, emig).

The only other forms relevant to dual --id that I can think of at the moment are pronominal --(m)mid, --ngid, --ð(id) (PE17:132).

Thanks Roman! It took me a while to get back here. School has started for me, yet again. Hopefully this is my last year as a college student!

1. What I think happened was that there was rim, and -li (like in Quenya). They combined, and we get words like gódhellim (WJ/364)
2. Good catch! Though... later on it would have become more and more difficult to tell the difference between -ss, -s, and -st, so they'd start to blend together.
3. Matt answered that question, but I add: it appears to have been a -t first. Thus hent, for "a pair of eyes". Also, I should probably include the diminutive forms -od and -ed in the section I made for diminutive suffixes.

1. Ah yes, of course!
2. Only at the end of a word, though.
3. Well, these forms are verbal endings where i is the thematic vowel of the conjugation. 

The thing is, most words originally ended with a vowel to which the dual t could be attached. For example, talf is from *talmā, with the dual presumably being *talmā-t(a), leading to *talvad. This is probably how we get galadhad, via galadā+t(a). (Actually, one might have expected *galadhod because of the long ā, so it must have shortened for some reason - either this was the original declension pattern, or it happened later by analogy to the shortened singular *galaða).
Hent in Etym belongs to hên, hîn which ended in -n (hence the long vowel, a replaced earlier variant is henn, hinn < *khendē) and could receive -t as an ending directly, but I'd say one needs to go word by word and see whether this is applicable.