Have I translated the following properly?
“Time’s a thief” = Tempus furtum est
Thanks in advance. 
Furtum means “robbery” or “theft.” Your phrase means “Time is theft.”
If you want to say “Time is a thief,” you might try “Tempus ereptor est.”
OK, thanks. A few more, if you don’t mind:
Pax via militaris = “Peace through strength”?
Sicunt aquilae = “Like eagles”?
Nemo et nihil = “[Trust] no one, [believe] nothing”?
First one should be “Pax via fortis”.
“Nemo et nihil” means “No one and nothing”. You can get away with leaving out some words, but not the main verbs.
“People called Romane, they go home?”
Actually, it was “Somebody called Romanus… they go… the house?”
Without a preposition (like “ad”) and without the accusative case, “domus” just means “the house,” with no indication that it’s a destination.
Consider "pax vi " (peace by (means of) force ),
or “pax viribus” (peace by (means of) strength ),
Or “pax per fortitudinem” (peace through ( or by means of) strength / courage / boldness ) , or “pax fortitudine” ( peace by strength)
For "trust no one / nothing " :
‘Credamus nulli’ (let us trust no one/ nothing )
Crede / credite nulli (“trust no one!”) . ‘Crede’ to address one person , ‘credite’ to give the command to multiple people.
Or ‘ne alicui credamus’ /
‘noli / nolite credere alicui’
( let us/ may we not trust anyone) and (do not trust anyone! )
Nihil (nothing ) is defective and has no dative (the case credere (trust / believe ) takes, so you have to use the irregular adjective ‘nullus’ (no).
Sorry about the horrible formatting, I’m on a phone and tried to indicate the other possible translations.
As indicated, you have a lot of options. Feel free to get more specific.
Per vis ad pacem.
Ut aquilae - not sure of the correct case of aquilae. Or you could use aquilae similes.
Thanks so much.
By “strength,” I mean specifically military strength/preparedness, as opposed to manly strength, courage, or force/coercion.
I also want to mean “[We fly] like eagles [to the stars].” I thought of using Sicunt aquilae/aquili ad astera, if that makes sense.
“Trust No One, Believe Nothing” would be a personal motto on a coat of arms.
Does ereptor convey the thought that it’s a sneak thief (but not necessarily a burglar, no B&E), as opposed to someone who just mugs you and takes your wallet and Rolex in the street?
As you say, there are different types of thieves.
“Ereptor” is more of a pillager or plunderer.
The word you want is probably “furunculus” (a pilferer or sneak thief).
So, the motto would be “Tempus furunculus est.”
Hardly seems sincere if you’re not doing the translation yourself.
My degree is in Russian, not Latin. 
Then Vi / vis / vim is not really the right word. You want Per arma ad pacem (cf Per ardua ad astra).
That might be something along the lines of ut aquilae ad astra volamus. Mottos tend to go for the infinitive which would be volare.
Missed this one. Belated thanks. 