How to get bitcoins back from cold storage?
- You can always use any web wallet application to sweep bitcoins from paper wallet to your web wallet. Remember you are sweeping ALL OF THE BITCOINS from the paper wallet while importing it in web wallet otherwise, you might lose the rest of the coins if you try to recover part of them.
What are private keys? Public keys?
- You will need public keys to accept Bitcoin payment just like your email address that you share with others to receive emails from them. On the other hand, you will need private keys to spend your Bitcoins just like a password for your email address which you use to read your emails.
Why transaction fee is this large?
- It depends on the network if there are high number transactions in pending in the network then you will probably need to pay little high fees to get your transactions confirmed. However please understand that you are making an international level of transaction and it's not that high in my opinion.
What is segwit (different topic but i saw it often in forum!)
See this guide:
What is SegWit?.
Hope that helps.