The words can often be used interchangeably. They have subtly different meanings that you should keep in mind when using them -- but don't assume a speaker or writer who is using them understands the difference!
"Assume" implies a bit more finality than "presume." It is more appropriate when a decision has been made, or is about to be made, with incomplete information.
"We didn't know how many people would be at the event, so we assumed that 100 chairs would be enough. (the decision was made)
"Since you didn't reply to my earlier email, I assume that you will not be joining us at the meeting." (implies that the speaker is ready to act without additional feedback from the recipient)
"Presume" gives a bit more room for the listener to correct the speaker. Using "presume" instead of "assume" adds an implied "but correct me if I am wrong" to the end of a statement.
"I presume you want chicken for dinner[, but correct me if I am wrong]."
In the past tense, "presumed" carries a bit of humility (if referring to oneself) or judgment (if referring to someone else), and it may imply that the presumption was incorrect in hindsight.
"I presumed that she would not object[, but she did object]."
"They presumed to know my intentions[, but they did not]."
"Assumed" is more neutral, and does not imply anything about the outcome of the assumption. If you want to communicate that the assumption was correct or incorrect, that fact will need to be made explicit.
"I assumed that the dog would not bite. I was wrong."
"She assumed that there would be enough cookies, and she was right."
The following examples contrast the two words and explain their implications:
Present tense:
"You have not told me what kind of ice cream you want. I assume vanilla will be fine."
(Even if the listener says nothing, the speaker will give them vanilla ice cream)
"You have not told me what kind of ice cream you want. I presume vanilla will be fine."
(The speaker would like the listener to confirm or reject the presumption. They will probably wait for an answer before giving the listener any ice cream)
Past tense:
"Alice assumed I would like chocolate cake for my birthday."
(The speaker may or may not have liked chocolate cake. It would be risky to guess without more information)
"Alice presumed I would like chocolate cake for my birthday."
(This is a subtly judgmental statement. Alice probably got it wrong.)
Final Disclaimer:
All of this is based upon present day, American usage. The words could carry different connotations in other countries or in older usage.
Person 2 is being dreadfully picky in my opinion. For one, to say that something "sounds very ghetto" as a negative is pretty insulting to anyone who lives in a ghetto. There are certain racial and social undercurrents to this statement that are far too complex to go into here as well. To get an idea for yourself, google "ghetto speech" and you will see a wide range of interesting material, as well as a good deal of hateful and racist commentary.
Suffice it to say that "where is it at?" as opposed to "where is it?" is somewhat "slangy" but also commonly used, at least in American English. Whether or not it is technically grammatically incorrect, it is common enough that most people just don't care.
Also, the informal idiom where it's at generally means a fashionable place where the most interesting things are happening at present. By extension, it can be used to refer to people, things or activities as well:
Studio 54 is where it's at.
Whole wheat spaghetti is where it's at.
Kant's Critique of Pure Reason is where it's at.
And so on.
Best Answer
outside of is perfectly fine in this case. It may be of a slightly lower register than alternatives like "other than" but it is often used in the same register as expressions like north of meaning more than.
I think my preferred translation in this case would be: other than