They are currently under heavy load of inquiries so you should expect a longer waiting time.
If I were to exchange BTC for ETH and if the exchange were to be conducted 'in-house' within Blockchain.info portal - they use Shapeshift - would this exchange go slowly due to btc current processing issues and would it be expensive to exchange?
I'm not sure but there are a lot of people complaining about them recently so If I were you, I wouldn't use them now.
Yes it'll be expensive compared to normal because of the network congestion, I think your deposit has to confirm in the nearest block as much as possible because I've seen a lot of users whoose transaction (deposit) got stucked for days and it's either "
trade failed" or stuck to "
exchange in progress"if it ever confirms after those days. As for withdrawal fees they released a list of it, since exchanging in blockchain.info is powered by shapeshift, I think these also applies to them
https://info.shapeshift.io/about