The red ENGG1000 is fine, because on some weeks you only have ENGG1000 from 2-4, and some weeks from 2-5. The problem is with COMP1911 Tute-lab, because it clashes with your ENGG1000 on some weeks.
To change classes, go into myUNSW, then to your profile, then vary enrolment, then update enrolment (or something like that). To choose a class to change, "swap" it. This will ask you for another class code. Put in the same class (i.e. if you want to change COMP1911, swap it with COMP1911; if you want to change MATH1141, swap it with MATH1141) and then choose the times you want.
I'm not sure what the procedure is for a permitted clash, but I think you might have to contact someone at the faculty to have a permitted clash (basically a clash that you're allowed to have, because you plan on skipping one of the classes involved or whatever).
Hope this answered your questions.