I am not sure about Hive Engine, probably nothing in there but I couldn't get there anyway because when I signed up for a Hive Key chain I only got so far when it said to do this or do that, so when I went back to ask which one I should do I never got a response back. It's be nice to get a Hive Key chain so I could power up in my wallet also.
Put in your posting key, memo key and active key.
After that you won't need to mess with your keys, again.
Well, unless you have to reboot it from scratch.
What you do to help with that is download the .kc file and save that.
Then if you have to reset the extension you just import the .kc file and you're done.https://hive-keychain.com/ is the place to get the download.
Does it matter my keys are the same ones from steemit?
Well, not practically.
If somebody compromises your keys they get both wallets if you don't change them.
I have no idea how you change the keys.
Peakd.com has an interface to do it.
Might not be worth the effort.
As long as you have kept your keys safe up to now, and don't use your keys in just any website that asks for them, you should be alright.