This offense is not an issue for the US. You were deported because of the overstay and not the offense. You may apply for a green card if you qualify after the exclusion period is completed.
The offense in Georgia is narrower than the equivalent offense in Canada as it requires the contact to be of insulting or provoking nature. This means that, unfortunately, you are criminally inadmissible to Canada at this time. You will have to wait 5 years after your probation period ends to submit a rehabilitation application to enter Canada. However, since you are or will be married to a Canadian citizen you are eligible to make an application to IRCC on humanitarian and compassionate grounds during this period to overcome your inadmissibility to Canada.
They would have to apply for an exception if the OP isn’t in Canada for H&C to work as well if I’m not mistaken.
Your wife would sponsor you for permanent residency from outside of Canada and then in that application, request that it be considered under H&C since you are inadmissible. Normal processing times are 1 year - however you should expect that your application will take longer because of your inadmissibility and the H&C request. She can remain in your country with you provided she is a citizen.
Given the nature of your conviction, I'd say there is pretty much zero chance of you being allowed to come to Canada at any point before the 5 years is up.
The approval of the humanitarian and compassionate grounds application is contingent on showing hardship to the spouse from the separation and the best interest of a child in Canada. Since the OP is not already married and no children or a household has been established yet this will be difficult to prove. Also, if the OP comes from a safe country and the Canadian spouse migrated to live with him this will be further used to counter H&C claims.
All US courts give warnings about effect on immigration status at the start of hearings, this is so that you can't withdraw your guilty plea later. In any case, that particular offense did not affect your immigration status you were actually going to be deported anyways as an illegal alien. Whenever someone is arrested in the US and put in jail, ICE will learn about this individual and if state dept. records show that person is an alien (as in your case as you had applied for visa), a detention hold is put on that individual's file to allow ICE to pick that individual after the case is concluded regardless of the outcome. The exception is a few U.S. jurisdictions that do not cooperate with ICE as commonly called sanctuary cities.
It is an assault charge against a family member, so yeah, it is serious. Hardship does not outweigh allowing a potentially violent person in the country. If the violence was against a partner or child, then it is especially relevant in a spousal app, H&C or not.
You are currently inadmissible to Canada. So yes - technically you are not eligible to apply for permanent residency at this time. As explained, you can try applying and requesting H&C considerations. However the chances of success are very low.
