1. Nutrition: As I said, nutrition is going to be at least half of your battle. If you are already struggling with energy levels (which will ultimately affect recovery), being in too far of a caloric deficit is not going to end well. That said, its not like you need to get this dialed in this freakin second. Just continue to work on it and improve. Two eggs aren't going to do much. You need to really try and focus on how much protein you require using online calculators (as a general guide), and work on figuring out how to get that. Protein powders, chicken breast, greek yogurt, cottage cheese, all that kind of stuff. Then fill in with fat and carbs. So, I would suggest focusing on a little bit at a time...Ie, first do protein...and work on getting more of it. Then start with the rest.
2. Lifts: Squats and Deadlifts work the most muscles in the body. They are huge compound movements that moves energy throughout your body (its why they are so tiring). There are other things you can do to fill in if you cant' do Squats or Deadlifts and you still want to work these, but it wont be AS effective. Machines, for the most part, don't allow for those big compound movements. The big lifts are the most efficent way to get stronger in the gym. The machines are good for some isolation work (and if you can't do one of the big compounds), but, if at all possible, shouldn't be how you hit primarily hit your muscle groups. Doing what you are doing, (ie, filling in a bit at the end of a workout), is the general wisdom of when to use them. So, its all good. Posteriour chain is hamstrings, glutes, back, and upper back. Getting this strong will make you strong.
3. Bigger/Stronger: Back to Nutrition. You need your protein dialed in. Two eggs isn't going to do enough. (Bigger/Stronger means at least maintance calories, but probably more).
4. 5x5. Whew. Yeah man 5x5 is very taxing. I subscribe to the school of thought of trying to do as little as possible to still see gains. If you are a beginner (Which most people are including me), 3x5 or 3x8 on the big 5 can work great. I would try and use a structured program though and not just wing it. Then take off what you can't due to your energy levels. I like Jeff Nippard's Fundamentals of Hypertrophy (a little more flexibility in the programming and substitutions), Mark Rippitoe's Starting Strength (strict in what it is trying to do with only one focus of strength in mind...for you, I think you need a bit of flexibility with some substituions available to you).
5. The Full Body is some good stuff. Really, its not until a little further in your training do you really need to start switching to push pull leg, or upper lower. But its really about what is working for you.
For me....I just went through a hypertrophy phase for the last 5 months. Put on about 22 pounds (obvioulsy some fat and some muscle). In about two more weeks, Im going to phase into a straight strength phase for probably about 3/4 months. See where that gets me. My squat is sad