"I can sense a disturbance in the air... A Stand user is sure to be near. Be very careful. [There's another person, too... I think this is someone that you've met before. I don't sense any violent intent, though...]" -Steel's progress report. The portion in square brackets is only said if the battle against Utah in Edfu is available.
If you're with Abdul and talk to one of the merchants on the southeast side of town, he'll be revealed to be an aquaintance of Abdul's, and they'll catch up on old times. Abdul's FP will go up by 1 afterwards.
Requirements: Abdul is in party, above event has been triggered
After you've met Khalid, a young woman will appear on the west side of the map on days 30~36. Talk to her for an event, and Abdul's FP will go up by 2.
Requirements: Iggy is in the party
If you buy shwarma from the merchant on the southeast part of town and Iggy is with you, you'll get an event. You can scold him for +2FP, ignore him for +1FP, or give him more for no FP but your bad karma will go down by 1. If your stand is Wildhearts, you get some extra dialogue after your decision.
Requirements: Jotaro is in the party
There's a merchant outside where you can buy Diamond C for 500G. If you buy it, however, he'll scam you by switching the bills in his sleeve, and it will actually cost 740G. If Jotaro is with you, he'll notice this, and demand the merchant pay back the money. However, the merchant won't fess up, so Jotaro will leave - on his way out, he'll secretly take back the 60G and 10x Diamond C, which will be added to your inventory. His FP will also go up.
Ultimate Junk Food
Requirements: Joseph is in the party
Talk to the merchant selling Sweets and Sponge Cake with Joseph in the party, and he'll tell you about American snack food and gain +1FP.
Requirements: Polnareff is in the party
Talk to the merchant in the hotel with Polnareff, and Joseph will crack a joke. Polnareff's FP will go up by 1.
In the southwest corner of the map, there's a woman in a chador. Approach her, and your ears will start ringing, decreasing your SP - talk to her to fight Amber. You'll get 1 FP with whoever was in your party after you defeat her and if your Stand is Deep Purple, you'll learn the Mirage skill.
Requirements: Have cleared the game 3 times or more, beat Utah in Hong Kong but not at the Harbor, current day is or is under 22, Sword Of St. George not in inventory
In the upper-right corner on the map is a familiar face who only appears if you're on your 4th playthrough and up and have fulfilled the above requirements. Defeat him for a Badge of Honor and the Rusty Sword, which opens up the path to the Sword of St. George sidequest. You'll also get 1 FP with whoever was in your party after you defeat him. If your Bad Karma is 7 or above or if you already have the Rusty Sword, you will only get the Badge of Honor.