Pick five: squat, deadlift, bench press, floor press, dips (weighted when strong enough), pullup (ditto), chinup (ditto), standing overhead press, SLDL, one handed row, barbell row (Yates style), T-bar row (can be done by fixing one end of a barbell in corner of room).
Just pick five and make sure those exercises cover the entire body (for example: squats, dips, chinups, overhead press, SLDL), and then focus on mastering them. That means doing just them with perfect form for at least half a year. No need to do anything else - no, not even curls (if chinups don't get you big biceps I don't know what curl will!). But you probably won't listen to me about this until you find out that that's all you needed once you get more experienced. That's ok.
Now, regarding your current routine, that's too much work for one session, so hopefully you were going to split that up. Also, doing deadlifts after a long session is dangerous - you have to be focused on your form unless you want a debilitating injury! Do them first or second. In general, arrange the exercises so that you work the biggest muscle groups first, or so that the biggest exercises are done first.
All in all, you can do your own routine, it's ok - but remove ALL of the curls. The bicep is a small muscle, it will grow tremendously from chinups and underhand rows, and no isolation work is necessary. Trust me, I'm an experienced iron-lover. I'd suggest you focus on some bigger compound exercises instead of mindlessly curling all the time! Also, you have plenty of overlap, for instance even though you have deadlifts in your routine you also have shrugs. I can't see the need for those. BUT, if you do them on different days it could be ok. Regarding the training frequency, 2 days a week is enough if you're working hard. Each time try to get a bit more weight on the bar (if you have access to really small plates, called "little gems", which are just a few pounds, add them each workout) and/or try to do more reps. This is called double progression: when you can do 2 reps more than your goal, increase weight next workout.
I see you're not focusing on the legs at all (you said it yourself in the question), so I'll suggest some safe ways to train them, ok?
Remember, the harder you work your lower body the better your entire body grows!
Try one legged squats. If you can't do them or balancing is a problem, grasp onto something - ideally a rope suspended from somewhere overhead.
Try sissy squats. This is a great movement for the quads and you're not crushing your spine here. You don't have to use any extra weight. Again, if balance is a problem, grip onto something. Even if it isn't hold on in case you lose your balance and can't get up.
Try wall squats. Basically, you 'sit' against just a wall. Your legs are parallel to the floor. Get a stopwatch and compete with your friends who can last longer. This is a very safe movement (and very painful!), and I really suggest you doing it.
Lastly, remember to rest and recover after each workout. Train hard (eat hard too!), enjoy yourselves, but then remember to have a life outside the gym. Training is meant to improve your life, not to become your life, and this applies to any lifter out there, no matter how experienced and hardcore.
I don't hope this helps because I know it does, I hope you listen! :)