It's been quite a while since I wrote that, so I had to look back a bit on what I did.
First, I need to point out that this was not some deeply thought-out conlang or anything; it was just an example I came up with for that post.
Aside from the innovations regarding person marking and tenses, it is essentially just Latin.
To address your questions:
First of all, what marks the infinitive mood?
I guess it would be -are as in Latin, though if I were doing this for real, I would shorten it to -ar at least.
I’m guessing the root is the bare infinitive?
The root is ambul-
You basically merged the infinitive with the future
I didn't merge the infinitive with the future, I merged the infinitive with habeo to get a new future tense, which is exactly what happened to create the French and Spanish future tenses. I just retained the /b/, which they did not, and I retained my regularized personal endings, which are something else in French and Spanish.
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Latin French Spanish This
amo aime amo amo
amas aimes amas amas
amat aime ama amat
amare habeo aimerai amaré amarbo
amare habes aimeras amarás amarbas
amare habet aimera amará amarbat
Essentially, in French and Spanish, the future tense is just the infinitive ending plus a personal ending that may or may not be different from the standard personal ending. In this agglutinative language, the personal endings are all regularized and the /b/ of habeo is retained.
Second of all, what made you decide to go with ar as opposed to er or ir for “arb?”
The infinitive ending for ambul- is -are. This is the same as Spanish.
And what happened to the -er and -ir conjugations, were they just replaced/eliminated entirely?
I would probably have them as different conjugation classes, though you could eliminate them if you wanted. It would still be agglutinative, but the exact ending added depends on the class of the stem.
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Latin French Spanish This
dormio dors duermo dormo
dormis dors duermes dormis
dormit dort duerme dormit
Latin French Spanish This
dormire habeo dormirai dormiré dormirbo
dormire habes dormiras dormirás dormirbas
dormire habet dormira dormirá dormirbat
It seems like what I have come up with now, the verb class determines which epenthetic vowel should be added, e.g. the personal endings are just -o, -s, -t, and the class determines if it should be a, i, or e. So maybe the future should be -rb(e) rather than -rb(a)?
why does the plural suffix have a nasal consonant?
I think the a was epenthetic. The plural suffix was just an on-the-fly regularization of -m(u)s, -t(i)s, and -(u)nt. Two nasals and two ending in s, so I just merged them to -ns.
Finally, I’m thinking a subjunctive mood would be formed from VL *ɛsserɛ and the imperative from *deβerɛ. Does this sound logical?
Let me get back to you on this in a bit. I'm not an expert in Latin and it will take me a bit of looking to answer this!