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You can remove both the figure environment and the center environment. figure is for floating, referencing, captions, but you don't use it anyway. Instead of \begin{center} and \end{center} just keep \centering , otherwise you get unnecessary space before and after it. \centering is for pure ...

I have some figures that are very big, so I placed them in landscape mode.

They are still too big for landscape mode so they get out of the page's margin. The problem is that the figure looks like it has a big blank space in the upper part of the page, so I would like to center the figure so that ...

In a book, LaTeX tries to keep the last line consistent throughout the pages. To that end, it may add vertical space between paragraphs, list entries, ...
So with different numbers of entries in LOF/LOL, you get different such added space.
If you don't want that, add
\raggedbottom to your preamble ...

I guess that depends on the class you're using.
For report class, you could try sth. like
\usepackage{etoolbox}
\makeatletter
\patchcmd{\@chapter}{\chaptermark{#1}}{%
\chaptermark{#1}%
\addtocontents{lol}{\protect\addvspace{10\p@}}%
}{\typeout{Chapters patched for list-of-listings.}}{\typeout ...

I guess that depends on the class you're using.
For report class, you could try sth. like
\usepackage{etoolbox}
\makeatletter
\patchcmd{\@chapter}{\chaptermark{#1}}{%
\chaptermark{#1}%
\addtocontents{lol}{\protect\addvspace{10\p@}}%
}{\typeout{Chapters patched for list-of-listings.}}{\typeout ...

A need my lstlistoflistings in the table of contents to be grouped by chapters and to use the same vertical spacings that are used in figures and tables listings.

What do I need to do add/modify to get those spacings?

Thank you.

There you go

I have a formula (using cases) centered and I want to take it to the left, but I don't know how to do it. Could someone help me? Thanks.

It worked. Thanks!!

I'm trying to write a function by parts but when I write everything and compile a (1) appears at the right side and I don't know why. Could someone help me?