Hardware wallets, at least some, can "hide" transactions, but eventually a transaction will be broadcast and be on a website.
Do not ever use an exchange to hold btc. You know the mt.gox scare, and an exchange could shutdown anytime and steal your btc.
I would suggest a hardware wallet with a tracker stuck on to monitor its position, but its up to you.
Yes but hardware wallets you have seed words..... so if it is broken or "waterlogged" you could always recover. I suggest putting seed words in a safty deposit box. If ever a problem with hardware wallet not working, or unusable you can use the seed words.
So still very secure and very usable on hardware wallets. Only barrier is price for some.