It doesn't look like there are plans to make this open source or give control of private keys to the users, I wouldn't recommend it regardless of the features it has.
They are giving recovery phrase.
https://support.abra.com/hc/en-us/articles/115003160368-Who-has-control-of-my-private-key-I haven't used abra but I have heard them many are using it and it's not only based on one country.
Many people use this wallet already but I never tried to make an account yet, there are so many positive reviews already but there are some negative too. And I only can't assure on this wallet/exchange in terms of security.
Me either, the negative one that you are saying might be the fees fiat->bitcoin.
It's unclear. It's like saying that you have a password on a website, therefore you can control over your funds. Unless these recovery phrases are owned exclusively by you, and is able to be imported to other compatible wallets other than Abra, it doesn't say much. Plus it's still close source.
Also you're dealing with something really sensitive here by using it which is fiat. When you have fiat and crypto mixed together you usually will not have as smooth an experience, and many problems could occur.
It only came out this year, in fact probably this month. I would first at least look for some reviews saying that it's legitimate before I start using. Even if I do decide to use it I would use with small amounts, as with any non-cold storage wallets.
