The initial "ei" is the genitive/dative form of the third person singular feminine personal pronoun.
This is a very common way to express sensations in Romanian:
Mie îmi este frig. - I'm cold.
Ție îți este foame. - You are hungry.
Ei/Lui îi este rușine. - She/He is ashamed.
Nouă ne este sete. - We are thirsty.
Vouă vă este scârbă. - You are disgusted.
Lor le este rău. - They are sick.
The Romanian adjective that properly translates "afraid" is "înfricoșată" and indeed you can say:
Ea este înfricoșată de ele.
Which is a perfect word-for-word correspondence with English. You can do that with pretty much every sensation. I gave examples here.
If you find this more comfortable because it matches English grammar, feel free to use it, but there's two problems:
1. Using the noun + dative of pronouns is by far more common and more natural; a native would probably use that.
2. The adjective needed is not very intuitive. (e.g. frică - înfricoșat; somn - somnoros) and similar forms change meaning: "fricos" expresses a general character trait, "fearful".
I am amazed by the sugestive sentences this app gives about romania. Like.. 3 question ago i got past a questiom about corruption which is very common in romania. I feel bad about the people that are going to learn this language with this exercises. Romania is a beautiful country, yea it has some major defects but that s only because of the people.. So please don t continue to put these kind of sentences or question because it s not fair and ok.