If you ask me, the workout is pretty good for the beginner's forums. You might want to check on the volume of the upper body workout - nothing fancy, just try to get it done around 1 hour.
To replace the lat pulldown with chin-up or pull-up would be great, as Petrichor said, but if you can't do that, this is a viable alternative until you become stronger. The additional bicep/tricep training is okay, but imho wouldn't be necessary if you do chins (my rule of thumb: If those make you train longer than 1 hour, cancel them).
If you want to do leg presses, the plank has its merrits. I'd do some front squats or Hackenschmidt squats instead of those two exercises, because squats train the same area. This reduces the volume a lot, but I personally would add some reps anyway, because I am a believer in high reps for legs. Damn, I am currently sprinting up a hill as HIIT and believe there is nothing better for the calves. If you don't want to do that, add some calf exercises...
I'd just completely cancel the HIIT training after normal training. Do that on the free days. If you're able to do an endurance training after the weight lifting, you're not doing it right. You should reduce the breaks. Personal note: After I bought a watch for my home-gym, I am training much harder. Give it a try.
I am also not sure if you're doing the plank long enough if you can do crunches afterwards
But besides the HIIT issue, I think it is a viable training program that will work for six weeks.
He has shoulder presses, which imho are great overhead pressing moves.
He has the good morning in there.