Bitcoins value does indeed affect the price of all altcoins since BTC/AltCoin trading pairs are the most commonly used and is usually the standard go to exchange pair on all cryptocurrency exchanges. So can Altcoin break all the relationship from bitcoin and run as a independent currency.
not if we study it from time to time until now, that's why something that is needed is great so that the market can be more independent. and it will take a lot of time until there are several altcoins that can compete with bitcoin. and if this happens then the market will be more independent without always fixating on bitcoin.