I'll offer something with a slightly different approach in an attempt to be more idiomatic in structure:
Si quis tibi occurrit, sua habet certamina abscondita.
If anyone meets you, they have their own hidden struggles.
Opening a sentence with a condition with si quis appears to be very common and feels like an idiomatic way to say essentially "...
The phrase everyone you meet seems like a idiomatic way to say everybody, so I would translate it as:
Omnis certamen certat quod nequaquam scis.
A simpler way to say it, although with less emphasis, would be:
Omnis certamen certat quod nescis.
quasi means "as if", non means "not", sit is the third person singular present subjunctive of esse ("to be") and thus can mean "it were", veritate is the ablative singular of veritas ("truth") and thus can mean "in truth, really", so the total phrase means more or less "as if it really weren't&...
I'm not aware of an established proverb, but if you want to convey the meaning "don't become angry, but [calmly] avenge yourself" you could translate noli irasci, ulciscere or (to keep the parallelism of the English phrase) ne irascere, ulciscere.
How many things are discovered while looking for something else? The translation given, in Comments, is incorrect.
For "dum" = "as long as", "dum" takes the indicative;
"haec feci dum licuit" = "I did this while (as long as) I was allowed".
The point is that for this translation ("as-long-as") the ...
I'm not really sure there is such a Latin proverb (maybe a phrase in some book, though I am not aware of it as well).
The closest I managed to find is English phrase:
I don’t care what you say about me as long as you spell my name right.
which has various attributions.
There is also a phrase in French:
Succès de scandale
which stands for success from ...
Interestingly both mittere and projicere are found in the Vulgate bible in the famous Joseph story where Joseph is thrown in a pit by his brethren (Gen 37). So on that authority alone I'd say both of your candidates would be sound choices.
However, it seems to me that demittere may be also appropriate: to send down; to drop; to let, sink, or bring down; to ...
So, the way the construction works is a simple predicate nominative with sum, infinitives are considered neuter singular, ergo. Any word for throw you want will work with the same construction:
"X est humanum"
X being, iacere, proicere, abicere, contorquere, torquere etc.