proper way to approach learning higher (university level) mathematics

Advanced mathematics tends not to have "tedious repetitive - mostly computational- exercises at the end of each section/chapter". Rereading abstract proofs is probably not a good way to use your time. Spend as much as you can on the examples. Take each theorem and see what it says about all the examples you know to which it applies. See how the proof works in each particular case. Get several books and mine them for more examples. The ones that occur in all the books will be the important ones. The rarer examples will be instructive too.

Study counterexamples too. See how theorems fail when one or more of the hypotheses is false.

You need not master section $n$ before reading ahead into section $n+1$. You can and should circle back from time to time. The earlier material will probably become clearer that way.

(Your English here is just fine.)