If i want to have access to bitcoin on the second exchange should I send from one to exchange to the other? and should i be able to move bitcoin from one exchange to another free of charge?
You will pay withdrawal fees,which are usually quite high.
In binance for example the fee is 0.0004 BTC (
https://www.binance.com/en/fee/deposit)
The best and most secure procedure is to hold your btc in your own wallet (such as Electrum.org) and move to exchanges only when you want to trade or convert back to fiat.
While your funds are in an exchange, the exchange is the one who holds your funds and if the exchange face any financial or legal problem your btc are at risk.