Kathleen, I do not have time to watch this video at the moment, but am going to make some comments anyway based on your references. Having not watched the video and lacking context, I may be off base sometimes.
Also, up front, I would say that when you choose an academic institution, you will have to play by their rules for writing academic papers, whether they are right or wrong, good, bad, or indifferent. In playing by those rules you will experience frustration, but perhaps also learn lessons that will serve you in good stead later on.
Certainly study Bibles are not be good sources generally, though there might be a specific reason to reference such in the right context. It can be all about context.
"Outdated resources" matter in some arenas, and not so much in others. The biggest problem with older sources is in the technical areas, where you miss out on recent discoveries, up-to-date information, and current challenges. If we are looking at the meaning of scripture, an older writing can be just as relevant as newer ones. In fact, in theology it is important to consider a range of writings across the spectrum of church history. The faith & practice of the church is a faith once delivered to the saints, committed to faithful men who were able to teach others also. Matthew Henry may be devotional and not technical, but if he said something best in a given area or on a particular subject, he ought to be cited. (I am speaking about the best Christian writing, and not academic papers that tell you not to quote him.)
"Free resources" have reasons to draw skepticism. What is it? Where did it come from? Is it translated or transcribed, and if so, who did it and how accurately, etc. However, this should not be anywhere near a universal ban. There are some great free resources on the web -- some of which include photocopies of original documents!
I think here the point is not about age (as in Calvin v. Henry), but simply about going back to original sources. Fact is, for some of the older theologians, one might likely need to learn other languages (e.g. Latin, Greek) to really be conversant in the original works. [As a side note, Calvin gets a lot of press, but I think one guy who is really misunderstood because of people reading what others wrote about him rather than what he wrote -- Arminius.]
Leon Morris is good. However, if LRC is strict about the ten year cutoff, you couldn't . That book is about 20 years old (unless there is an updated version of which I am not aware).