Shivams, I agree with your assessment that Zorich is more comprehensive than Rudin, taking both volumes of Zorich into consideration. Also, I would say that if you are enjoying this book, there is no reason to switch to reading Rudin instead, whether you intend to use the material for engineering, pure math, or anything else. Just keep reading Zorich.
Rudin's main advantage might be its brevity. This is an advantage only for people who already know most of the material that would be taught in a very rigorous, very complete multivariable calculus course. For some, it might also be an advantage that Rudin introduces topology early and can then use this wherever it helps an argument go more smoothly.
The only major topic I see that is covered by Rudin but not by Zorich is the Stieltjes integral. Rudin's treatment of some topics, such as differential calculus in several variables, is clearly insufficient for practical mastery, even though in some cases you will see the main theorems presented. In the case of multiple integrals, even the theory is insufficient.
Although Zorich starts off more concretely, by the end he includes more abstract material than does Rudin, such as general topological spaces (as opposed to just metric spaces), differential calculus in normed vector spaces (as opposed to finite-dimensional ones), and smooth manifolds, not even touched on in Rudin.
How you study I think depends on the facility you have with the subject. If you can manage the exercises in Zorich's book, just keep reading. If you'd like lots more exercises in analysis with solutions, you can have a look at the problem book by Demidovich, which has an English translation. Kaczor and Nowak also have a problem book that might be worth looking at. One advantage of problems with solutions is that they draw attention to points in which your own solution had an error in it or wasn't detailed enough.
In terms of time, it's very hard to say how long this ought to take. However, I'd say that the content of this book covers almost everything you'd learn in analysis before your final year in a strong BA program in math at a Canadian university, and probably more in depth as well. If it takes you a year to master the content in this book, then you're doing well. Once you've also learned algebra, you'll have an extremely solid foundation for studying more advanced topics.
Correction: There is a chapter at the end of Rudin with a brief introduction to the Lebesgue integral. This has no parallel in Zorich's book. However, I still find Zorich more comprehensive overall.
Other than Rudin's analysis text (the first one), I've read Robert Strichartz's "Way of Analysis". Strichartz gives you a lot of motivation and information for most of the concepts, while Rudin just gives you enough for you to do on your own. I favor Rudin's text much more, since I enjoyed the effort required to fill in the gaps and thereby making you "do" a lot during the reading. Additionally, Rudin has a style that I believe many enjoys, for most of his proofs are elegant and stylish. Strichartz will explain much more during, before, and after a proof, but sometimes I feel that his explanations becomes a bit too wordy and too cloudy over the main point. Take it this way: Would you rather try to find a dull sapphire in a messy hay sac, or find a beautiful diamond hiding in a small pile of needles? (one requires sheer effort for something "okay", while the other requires much more effort and care, but to obtain something rather nice.)
I realize that you want to read a more friendly analysis text before Rudin's, but have you considered reading Rudin's and supplementing it with one of the texts you've mentioned simultaneously? If you read Rudin and find that you have a lot of questions, then use the supplements and this site; questions will only help you.
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Herbert Amann's analysis which has three volumes is more detailed than zorich's analysis.However, I think it is too difficult to read.