Is it possible to pick C01 (by Haskell) and T02 (by Marikova) as a combination of lectures and tutorials for Math 1a03? because the T01 conflicts with my enviro 1g03 course.

SOLAR will do that automatically for you after you choose your courses.
When you select your courses the first time SOLAr opens, you only get to choose which semester you want to take the course in.
Then SOLAR will be closed for a while and will make your timetable for you thats conflict free. When SOLAR opens again in august, you can then switch/select/customize which core tutorial and lab sections you want.

simple answer: yes. your cores and tutorials don't have to be the same number.

Yes definitely. You don't have to pick cores with the same number as tutorials. The only time when you have to choose the same number is with, for example, Chem 1A03. Labs and tutorials alternate every other week, so they have to be in the same time slot. Other than that you're free to take your pick

Just thought I'd point out that even though a tutorial says "MARIKOVA" or "HASKELL" it almost certainly will not be run by the professors themselves. You'll be getting a TA to deal with a little more closely than a professor.

So that being said, unless you're going to have some sort of manditory attendance, participation or weekly tutorial quiz, (all unlikely in Math 1A03) then you can pretty much attend whichever tutorial you want to. If one week you can't make it to T01, then you can go to T03, etc.