Why is it necessary to put "pe ea" at the end? Is it possible to merely put" eu o urmaresc" ?
It's not necessary. It's just a stress mark, like "I am following HER, not another woman".
Everywhere I look, "to follow" is "a urma" which is is conjugated : Eu urmez, tu urmezi,
el/ea urmează, etc. Is Duo's translation a mistake?
In English, the verb "to follow" has many meanings.
If you mean "To go after in pursuit", "To keep under surveillance", "To watch or observe closely", "To be attentive to; pay close heed to", then you use "a urmări" in Romanian.
If you mean "To come or go after; proceed behind", "To move along the course of; take", "To accept the guidance, command, or leadership of", "To adhere to; practice", "To come after in order, time, or position", then you use "a urma" in Romanian.
It appears that "to track" is close in meaning to "a urmari", exactly as Lurch M explains. So this sentence does utilize the conjugation for "I track . . . .", if I am not mistaken.