Does multibit HD still work offline and is it safe to connect to transfer funds?

I am new to the whole bitcoin situation and have some super noob questions. I watched this tutorial for creating a multibit coin wallet on a USB stick . I successfully made my wallet on a USB stick and made a backup on another, however I got the newest version of multibit, which is multibit HD and it appears that you can’t create an address while offline. I played with it for a long time and can’t figure out where to generate addresses or QR codes. I finally decided to connect to the internet and clicked on the buy bitcoin and it took me to Glidera and created a address and a QR code for that transaction. My question is, is my account now not secure because I connected to the internet? Can I use the address created for that transaction to receive bitcoins I get or buy from another source, and if I can’t connect my wallet to the internet without breaching it’s security how do I spend my bitcoin(do I have to create a new wallet offline every time I spend any bitcoin)? Sorry for the longwindedness of that post, but thanks for taking the time to read this!!

Recent Questions – Bitcoin Stack Exchange