Noob question regarding my coins on Binance

Hi there,

Im new to crypto and I have placed part of my pension savings into XRP and ETH on Binance.

Since the recent news items about Binance have come about, Ive been researching what to do, and Ive noticed that most peoples advice is to get everything onto a hard wallet (which Ive researched and Ledger Nano S seems to be a decent choice)

I had no idea that this was the normal thing to do anyway, and was set to leave all of my funds on Binance.

Im sorry to be so clueless, but, when I 'move' everything onto Ledger, its then no longer 'on Binance', and then in the future when I need to trade back into fiat, I can go from Ledger and then onto any other exchange such as Coinbase, exchange into Fiat and then withdraw to my bank from there? And in the meantime if Binance goes tits-up, it doesnt affect me once Ive associated it with Ledger?

Also are there fees to move to and from Ledger?

Thanks in advance, my eyes are going blurry from researching here and Ive got an information overload happening, I figured it would be better to just ask due to the urgency Im feeling right now