Yes you are safe using your active key on Busy.org (slightly easier or more intuitive user interface than Steemit, and posts are mirrored to the other site, no matter which one you use). So long as SteemConnect is your intermediary, you are safe giving it an Active or Posting Key. Don't use your master key except on Steemit when you're transferring funds, etc - i.e., only when steemit.com asks - and always double check the url bar. Occasionally you'll hit a phishing link that looks like Steemit, that wants to trick you into signing in, but they're stealing your pw to drain your funds.
Almost any question you have can be answered by Googling, just put Steemit in the question and you'll find usually lots of matches - pay attention to the more recent ones as things can change.
Enjoy!