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What are you talking about? Your statement is a jumble of contradictions. A hardware wallets are designed for the exact opposite. They are secure, offline storage solution that you dont need to constantly fiddle with.
Offline? No that is not true. Most hardware wallets require a connection to a computer and internet to operate, so that can not be considered offline.
No, you are wrong about this. Most hardware wallets (or at least the ones I have laid my hands on, and I have had quite a few) can sign transactions completely offline and without using the internet.
Read what Cricktor wrote below your post, he explained it well so there is no need to repeat it.
Absolutely no. What he described is how Ledger works, and if you consider Ledger an offline wallet you are being crazy.