Praise be to Allah.
Praying four rakahs after Jumuah prayer is the opinion of some Madhhabs, and has
nothing to do with staying in Makkah or far away, or being in an Islaamic country or
not, or whether or not there is a khaleefah. The existence or permission of a khaleefah
is not a condition for Friday prayers being obligatory or valid, according to Ahl
al-Sunnah wal-Jamaaah. (Fataawa al-Lajnah al-Daaimah, 8/187)
Having dealt with what you have heard from people who have no knowledge, but who are unfortunately in the position of "imaams," as you said, we move on to the basic issue of offering salaat al-dhuhr after salaat al-jumuah. Our answer to this question is that the truth is the opinion of the scholars, most of whom say that there is no basis in shareeah for offering dhuhr prayer after jumuah prayer if a person has prayed jumuah. The one who misses jumuah or does not attend it because it is not an obligation for him or her, such as women, sick people or travellers, must pray dhuhr. It was never reported that the Prophet (peace and blessings of Allaah be upon him) or any of his Companions prayed dhuhr after praying jumuah. If he had done so, there would be reports to that effect.
We ask Allaah to give you and us help and strength. May Allaah bless our Prophet Muhammad .