Legacy vs. Segwit

Hi,

Could someone clarify the following questions for me please?

1.) In order to have access to BTC on the Segwit chain, I have to send myself some BTC from the legacy chain to the Segwit chain?

2.) If i want to send myself some BTC from my ledger to an exchange, for example Bittrex, can I send myself Segwit BTC onto the bittrex address? Assuming that the bittrex address is still a legacy address.

3.) the lowest current transaction fee is around 3 dollars on the Segwit chain and 9 dollars on the legacy chain for the transaction I want to make; Should I just wait to make a transaction for fees to go lower or will they stay in this region? A tad bit much, no?

Thanks for answering the questions!