Can I trust MyEtherWallet?
It is considered generally safe, but if you care about your stash, buy a ledger nano S and just use myetherwallet to set up transactions that you sign with the ledger. Make sure of secure domain.
Is MyEtherWallet app safe?
MyEtherWallet is legit and safe – but make sure you follow the safety instructions on their website. Be very wary for phishing sites, always make sure that the URL is correct.