some clarifications on cryptocurrencies

I'm new to all this so this may apply to many people. 

I had a post here on steemit that generated about 40$ so I thought I have some funds to play around and check various stuff:
I converted that to bitcoin in my online blockhain.info wallet.  SBD to BTC - forgot what service I used for this one.

I experimented with ethereum downloaded mist and waited for hours for that thing to get up and running and finally got my eth address. deposited about $20 worth of btc to this ethereum address using shapeshift. 

But then it tells me I can't see the transactions so I have to create a transaction wallet.. (really confusing, I didn't really get it but ok) So I click that thing and it added a fee that ultimately cost about 7$. 13$ left in the ethereum wallet.. mmm okay but since I don't really want to wait for 30+ min everytime i start up my "wallet" I looked for online alternatives. And I found ethereum-wallet.net.
By now the value of eth has increased so my eth wallet went up from $13 to about $17 in value. I transfered it to my online wallet. 

Today, seeing as the value increased I decided to switch back to BTC so I used shapeshift again, and transfered all I could back to my blockhain wallet. 

I ended up with $13 in the bitcoin wallet. I don't know what to say about this, but even my greedy bank doesn't charge such ridiculous fees when I use their services or exchanges or withdraw from  "competition" atm(s).

Is this normal ? this is the last shapeshift transaction from my online eth wallet to my online btc wallet : https://blockchain.info/tx/09e3ab9e6d3eec7af1086a54a85fb772858be541f2bd1966cc7d90ef96f71500

I started with $20 something worth ethereum and ended up with $13 worth of btc. What's goin on here ? shapeshift takes that much tax fee ? 

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2'nd point, 

What are my options for offline wallets that DO NOT IMPLY downloading tens of gigabytes of blockhain and waiting for hours and hours to use ?
I want an offline secure super fast no bloating quick n easy and to the point btc wallet. Suggestions for other currencies welcome. 

Thank you