I am able to translate the following just fine; I have some grammatical questions relating to it.

The phrase I am interested in is the old, "Homo sum: humani nil a me alienum puto," appearing for the first time (I think) in Terence's (Terentius') Heautontimoroumenos (The Self-Tormentor). "I am human: I consider that nothing human is alien to me."

Dropping the "Homo sum" (I am human) and the "puto" (I think, I consider), we have just "nothing human is alien to me." That would make a great Latin motto; maybe even better would be "nothing human could be alien to me."

Doing a little digging around on the untrustworthy old internet, I find all of the following "versions" of the phrase, quite variously ascribed (to Cicero, Tertullian, etc.):

-Humani nil a me alienum (probably the original?)
-Nihil humanum a me alienum est
-Nihil humani alienum
-Humani nihil alienum
-Nihil humani mihi alienum est
-Nihil humani mihi alienum

I know enough to know that in an inflected language word order matters little if at all, so at least some of those are grammatically exact equivalents. I further assume that "nihil" and "nil" are exact equivalents.

But can someone explain to me with confidence whether the sense is retained if the "a me" is dropped? What is the effect, if any, of adding the "est" (is)? Is "mihi" a different and correct way of saying "a me" (to me)? How can "humanum" and "humani" both be correct?

What would be the most parsimonious, elegant way of saying "nothing human is alien to me"? And of saying "nothing human could be alien to me"? And "nothing human can be alien to me"? "Nothing human is alien to us"?

Many thanks in advance, o wise Latinist.

1.In his Latin dictionary published by Amsterdam University Press, Prof. Dr. Harm Pinkster -definitely an expert - explicitly mentions that "alienus" can be combined with either dative (mihi) or with ab + ablative ( a me). Mihi alienus "not akin to me" however might in some contexts get the connotation of "hostile to me".
So probably nothing wrong with "Nil humani mihi alienum" as a more concise rendering of Terence's line. Briefer than "alienum a me".
2. "Nil humani" ( genitive structure) is probably best rendered by a relative subclause: "nothing of that which is human". Or: "nothing that is of man".
3. At http://www.xs4all.nl/~josvg/cits/terence/ various other English and also non-English translations are mentioned.
4. For a "concise motto" " Nil humani mihi alienum" does not
require the addition of "est". First of all "est" is not what Terence wrote, and secondly it adds no meaning to the line. Just a copulative verb unnecessarily lengthening the line.
I would translate that motto as: "Nothing of man is alien to me". Better than "strange" because I may be "amazed at" what is of man, but still recognize it as not "alien".
5. The full line as written by Terence I personally would translate as "I am a human being, and count nothing that is of humans, alien to me". Rather than "I am a man", which sounds as though it excludes women.
That would be my "subjective choice". Hopefully an "enlightened" one, but definitely an imperfect one for various reasons.

A very satisfying answer; many, many thanks.

A few subsidiary issues do remain, for you, flem-ish, or for some other intrepid Latinist, viz:

Are the case inflections adequate to convey the same sense in the absence of either "a me" or "mihi" -- that is, could it be "humani nil alienum" tout simple?

And: what about the variant I saw with "humanum" instead of "humani"? Wouldn't that necessarily change the sense? Or would the change be as simple as keeping human- genitive, but now in the singular, or something?

And: How would one say "Nothing of humankind is alien to us" (rather than "to me")? If one is going for a family motto, one would want alien- to be in the first person plural dative/ablative, right? And maybe add a different pronoun in place of "mihi/a me"?

Again, many thanks for the authoritative reply!

In plural "mihi/a me" becomes "nobis/a nobis". No problem there.
The subtle semantic difference between "Nil humani" and " Nil humanum" is in itself no problem either.
As a phrase "Nil humanum a nobis alienum" is o.k., but to me it does not sound very euphonic to have that "-um" ending twice. It is very "recognizable" however to users of the English language.
As to rhythmic pattern my choice would be:
"Nil humani a nobis alienum". With a short pause after: 'humani'.
In that way the phrasing stays fairly close to what Terence actually wrote and the motto can be understood as either:
"Nil humani a nobis alienum p-u-t-o or e-s-t".
"Puto" sounds a little less self-assured than "est".
"I consider nothing human is alien to us"(putative statement) vs "Nothing human is alien to us"(definite claim).
I would leave it open to the "reader" of the motto how to fill out the line!
Another variant might be:
"Nec enim nobis nil humani alienum".
Nec is a so-called "double negation" and strengthens "nil".
Enim can be understood as: for; indeed.
It might add some irony to the motto, but it lengthens the line.
A little shorter: "Nec nobis nil humani alienum"
My ultimate choice would be :
"Nil humani a nobis alienum".
But that's a subjective preference. "Nil humanum" would be more transparent to non-Latinists.

Brilliant stuff, just brilliant. Many thanks, again. My cup of gratitude overfloweth.