So לפני can mean both "before" and "before me"?
Do not confuse between "Lif-nei" and "Lefanai" (both are written as לפני"). "Lif-nei" = "before". "Lefanai"="before me"
Sometimes "before me" is spelled לפניי to disambiguate.
Is it possible to use something like "לפני אותי"?
No. You have to use the pronominal suffix in these cases.
כתבתי: אתה חייב לשלם לפניי. היה צודק. :)
אני גם חושב שזה נכון
It's correct, if it's not accepted you can report.
atah tzarikh leshalem lefanai
יש לך לשלם מולי should be also accepted, shouldn't it?
No: יש לך means "you possess", not "you must".
Also מולי means "in front of me" or "opposite me" (location-wise). In this sentence "before me" refers to time, not location.
When would you use this sentence?
Could קודם לי work here too?