Skype for Business compatibility with regular Skype

I have been having some of the same issues. I have however found that you can schedule a "Skype Meeting" and invite people who do not use Skype for Business. They can access the meeting by using the internal link within the meeting invite. It opens up within their browser and they can join in. You can give them 'presenter' access and you can then all share desktops, documents, use the whiteboard etc. You can also record it (which i regularly do, and then post the video to our external Yammer group).

Skype for business will allow you to have a 'normal' skype call/video call with a Skype member; but you wont be able to share desktops/documents etc. This is also the case if you use the "meet now" function within Skype for Business. So you are best to schedule a skype meeting and have everyone join that way (then they don't have to worry about having any skype access)