I did not watch the workout video (yet) but I watched your warm up video. I was concerned about your form during some of these exercises but I see that you are looking to improve them.
Obviously, a professional would help you a lot (in the sense that they could show -instead of textually describing- the moves) but I will do my best.
Here is what I think needs the most work. (Top 3)
- Lunges : You are losing your balance because your center of mass is not well situated (you are at ''physical disadvantage'' because of your form). This is mostly due to the fact that your knee go way too forward. Hopefully, this is easy to improve : when taking the forward step, try to reach a bit further in front of you. As for the other knee, make sure it softly touch the ground. That should do the trick.
- Squat : Your squat technique is very poor (although I have not seen the back angle, by looking at your knees, I suspect you round your back). You can see that your knees shake (may be they are not used to the new tension) and you go, again, way to forward (a sign of weakness in this case). I suspect that the way you place your hands has an impact on your form. Try placing your arms in front of you instead. When starting the move, bend a the hip first and try to ''sit back'' (use a chair if it's needed). Foot placement is may be a tiny narrow (nothing bad with it but it could impact your form). Try to use a wider stance (may be 5-6 inches wider) and angle your toes 45degrees outside. This usually helps a lot.
- Pushups : You can see that the back angle is not right. When lowering, you also lower your core area before the working muscle. This means that your core is not strong enough compared to the working muscles (chest/arms). This can be dangerous because the tension is not well transmitted through the body (you end up forcing in a weird position that could result in a back injury). To remedy, here is what I would do : Try wall pushups. This may sound ridiculous but it is a very awesome move for beginner. It teaches coordination (lowering the upper body before the midsection) and it still provide enough tension in the upper body of a beginner to improve strength. I would also work on push up planks (make sure you are holding the right position). Planks, if done correctly, will show you how to contract all of your body as if it is one big unit. This is a must if you want to do pushups.
I quickly looked at your workout template and it looks like a somewhat good beginner workout. I am just very concerned about the lack of vertical pulling. I believe that pullup work is a most (I am biased, it's my favourite exercise).
Why is it a must? Pull ups are very useful. They build the back like no other move (hypertrophy wise) and they build very useful strength like no other move. On top of that, once you get good at them, there are so many variation that you never stop progressing. (And, no, I am not refering to weighted pullups as a ''harder'' variation... I am talking about L-pull ups, muscle ups, etc. Granted it is not for everyone, it's still fun to train with a move that is so versatile).
I would either remove the pull over or the rows to work on pullups. The good news is that I am writing a small guide to help people reach their first pullup at the moment. It will be on my website this week. You should check it out!
I hope my tips were helpful. There is nothing more fun than working out. It's a real pleasure to train and achieve goals. There is just no other feeling like this (or, i would not be studying exercise :) )