Does the Fighters Guild still exist in the 4th Era? If so, is there any reason given in lore why it is not present in 4th Era Skyrim? Did it ever exist in Skyrim?

AFAIK there is nothing in the lore to suggest the Fighters Guild no longer exists. I don't think Skyrim ever had a Fighters Guild, as the Companions were already well established at the time the Fighters Guild came to be.