Yes, this makes it very dangerous and most people that write about these topics don't understand really what this means. I would never use a closed source wallet, and there is no need for a wallet to be closed source.
There is a difference between the safest wallet and the safest wallet for beginners. Wallets that let you take custody of your coins (in other words, they are not managed by a custodian, platform or third party) are safest generally, because you have complete control. Though with great power, comes great responsibility. If you are a newbie, you will be subject to a variety of risks that custodians may prevent for you (address poisoning attacks, malware, hacks, incorrect usage or mistakes).
Yes but also if you use a custodian you are subject to new risks. How many people have lost money from exchange hacks or their exchange accounts being hacked?