Being open source allows the client to be peer reviewed. It also allows you to download the source code and compile it yourself in case you're worried that the source code is different from the distributed version of the application.
No third-party has access to your private keys. Private keys are both generated and held locally. Additionally, as it is the official client, it is the most actively peer reviewed wallet.
As of December 2015, the entire blockchain is over 50GB. The growth rate has been more or less linear for the last year when it grew in size by about 25GB. Thus it's reasonable to expect the blockchain to grow to 75GB by the end of 2016 and so on.
Since the wallet downloads the entire blockchain the first time it loads, which as of December, 2015 is over 50GB, it can take a long time to download.
Electrum is a hierarchical deterministic wallet meaning both public and private keys are derived from a seed. In case the wallet needs to be recovered, you can do that using the seed. Electrum uses a 12-word mnemonic passphrase and asks you to re-enter the seed the first time it generates the keys to make sure you understand the process.