Yes and transaction fees aren't evaporating your cryptocurrency savngs in Bitcoin I guess?
That is right. Savings means it's not being transferred, therefore no fees. A wallet from 2009 will have exactly the same number of Bitcoins today and forever.
So if a miner charges you 100 BTC to send a transaction then you have to pay.
Wrong again. No miner can force a fee on any transaction. If a transaction doesn't meet a miner's fee requirement, then the transaction will simply be mined by someone else.