Once you want to sell your cryptocurrency for fiat, how would you do it?
Would there be any liquidity problems with semi-big sums e.g. 20.000$?
There is no problem usually about exchange in this platforms, especially if you become verified member. For example Coinbase (for some countries) exchange crypto for fiat, also Neteller, and Payza.
This is not true.
You SHOULD be aware of liquidity problems. Coinbase, specifically, has weekly sell limits and it's based on your current level of activity and how much identity verification you've provided them. At my level of verification and sell limit it would take me over 3 weeks to sell and withdraw the amount of currency you're talking about...and of course Coinbase completes all the necessary documentation to make it known to the Federal authorities. I'm not opposed to that last bit, but it's worth knowing.
You need to plan your sell/withdrawal carefully based on these sell limits and the urgency or demand you have to get that currency out of cryptocurrency and/or out of the wallet and holding exchange.
Good luck to you!