The lettings agency should in fact agree to your sub-letting the apartment too. I would check with them if they know you're sub-letting it.

Legally, she cannot charge you more than 30% of the rental charge that she is paying. That's why the lettings agency should get involved and would ensure this. They legally need to agree the rent that she is charging you.

Regarding your deposit of the flat, you should have opened up a proper deposit account (and not given it directly to her).

Hope you sort it out.