Electrum has a mobile app if you want to keep it to a mainly focused mobile app like Trust wallet. But that's also only for BTC keeps.
As for your USDT, what chain is that? There are several wallets that you can keep that if you don't want to keep it there like if it's on ERC20, Metamask and MEW would be enough and the risk is on how you'll keep your private key.
Yes, it is very safe and secure to hold your btc and crypto-currencies for long time as you can. It has private key like myethreumwallet. I hold many coins in trust wallet. But dont loss your private key. If you lost your private key, you lost your coins.
Just to give the idea, TrustWallet is closed source and owned by Binance.