Overall answer: no.
I struggled with the same problem as you for quite a long time and, in hindsight, I think I could have spent my time more wisely. Here are my current general guidelines at the time of this post. They may or may not work for you. The overall philosophy I employ is that exercises are usually there to get you comfortable with the material: you are probably usually expected to remember the theorems and (mostly) forget the exercises once you have done them. I expound on this below.
How do you read the mathematics books and make knowledge on your own?
Nowadays I spend more time thinking about the material in the text than doing exercises. I treat the theorems as problems and try to see how far I can get in proving them before reading the proof. Importantly, I don't spend all day doing this! A good strategy might be to set yourself a goal, such as "I want to get to such-and-such page by the end of the week", and pace yourself accordingly; if you spend thirty to forty-five minutes thinking hard about a theorem and having no ideas, perhaps take a peek at the proof and continue from there (alternatively, skip that proof and come back to it later).
If the book has examples in the text, read and understand as many as you can. Otherwise, be sure to allocate generous amounts of time towards coming up with your own examples. Note that this is not necessarily easy, and is arguably the most important stage.
Finally, if the book has exercises, be sure to do at least some of them and try to understand the general idea of the rest. Don't be afraid to ask and try to answer your own questions which might be inspired by some of the exercises.
One downside to this method is that it doesn't work for all books and all subject matters. Some authors place key theorems in the exercises and proceed to use them later, expecting you to have proven them yourself. The hope is that for each topic there exists a book for which this method is not useless.
Another downside is that, in rare cases, too many of the exercises are interesting (this appears to be the case with Rudin, among other books)! In this case it's definitely up to you how much time you spend on the exercises. Allocate time according to how interesting you find the exercises and how comfortable you are with the material in the text.
Is it absolutely recommended to prove everything and solve every problems in the book?
If you can do this and still lead a comfortable life, then by all means do so (if it doesn't hurt, then it can only help, right?). Unfortunately, attempting to do this will probably make life less than comfortable for you, so I would advice against being this extreme.
However, the point of this "advice" is that you should get as comfortable with the theorems and the examples as much as you possibly can, and this is good advice. I would advise just thinking about stuff as much as possible. Thinking about maths in the shower, on the way to the shops, while cooking dinner, etc. will get you used to thinking about the topics that interest you.
Also is it recommended to devote more time to the problems than exposition preceding the problems?
This heavily depends on both the book and the reader. However, if you prefer to come up with your own examples and fiddle around with the theorems, and if the book you are working from is not expecting you to prove key theorems in the exercises, then I would say this approach is a good substitute for doing exercises.