A lot of people would tell you to keep your left up, to keep a higher guard. I don't subscribe to that belief, but you do have a tendency to drop your hands and punch from the waist. You are too square up to do that; turn sideways. Get your left hip and shoulder up front. And keep your right hand home. The huge majority of your defensive work is done by the right hand, ideally. It catches the jab and it blocks the hook, the right elbow protects the body. Also, if you keep the right hand home, you can shoot it when you punch.
You also have a tendency to walk forward after your right hand, to bring your right foot up, like a baseball pitcher, you know? That will get you hit really hard- watch Tyson v Botha.
Finally, you could be much better inside very easily. First, get more sideways, the left shoulder and hip into your opponent. That vastly improves your defensive position. Second, throw your left hook. I can guarantee you that, in the not to distant future, you'll be asking why you can't land a left hook. Watch the video you just posted. You are in position many times to put the hook into the body and you don't throw the punch.
Last, the guy you were working with seems to know a bit about fighting. He gave you good work. That is very valuable.