Since you know 4 languages, can you take a proficiency test in several of them and list these?
Applying for Global business at Lincoln Center may be easier but not sure it’d be interesting to you to travel so much (London, China..) or perhaps indicating it as your secondary concentration of interest (for the concentration you only need one semester abroad wherever you want, or two summers abroad.)
https://www.fordham.edu/undergraduate-admission/majors-and-minors/global-business/
It’d match your linguistic knowledge and reinforce your application.
Why no ACT/SAT score - it’d go a long way toward helping alleviate any doubts created by your downward trend.
You can say you were missing your family junior year because you had not seen them in (30) months and the burden&sadness caused you to lose focus on academics but you’ve now found ways to overcome this through (zoom, package exchanges, whatever) .
Being full pay will help but if that F is on your transcript it’s going to look bad. No escaping that fact.
That being said rigor and GPA are okay - B+/A- is decent, and you’re applying ED + are full pay.
So I’d guess your odds are 50-50, perhaps even 60-40 depending how much they’ll value full pay ED.
(ED is binding, meaning if they admit you, you’ll attend - and your parents are willing&able to pay your full costs. Correct?)
Where else are you applying?