Escaping Issues

The point of escaping is to make sure that when a value is output, it cannot output anything malicious, or that would just break the markup of the page. For example, when outputting a variable, you will want to escape certain characters so that the value can’t unintentionally open or close HTML tags, which could break the layout of your page, or even output a <script></script> element that could run malicious JavaScript.

WordPress VIP’s documentation has a great overview of the concept, with examples: https://wpvip.com/documentation/vip-go/validating-sanitizing-and-escaping/

Regarding your specific examples:

Must I escape variables, if it is, how can I do it?

For example: global $redux_demo;

in this code:

    if ( class_exists( 'Redux' ) ) {
        global $redux_demo;
    if ($redux_demo['button-set-single-archive-services'] == 2)
    {
        get_template_part( 'demo-archive-services' );
        die;```

No. Not all variables need to escaped. Variables only need to be escaped when output. $redux_demo is not being output, so nothing here needs to be escaped.

Is it true escaping?

<?php esc_html_e( 'Our Services', 'hekim' )?>```

Yes. _e() is a function that allows the 'Our Services' string to be replaced by a translation. This means that you can’t trust that the output of this line will always be safe. Therefore it needs to be escaped. esc_html_e() is a function that automatically escapes with esc_html(), after running _e() to allow the text to be translated.

Functions start with the, need escaping or not?

For example : <?php the_title(); ?>

If I change these functions with the functions start with get, do
they need escaping? Is there any difference about output with
functions start the and functions start get?

As a general rule, built in functions that start with the_ don’t need to be escaped, but functions starting with get_ do need to be escaped. For example, the_permalink() uses esc_url() to escape get_the_permalink() before outputting it.

Why this escaped function doesnt seem?

After escaped this phare, it doesnt seem.What is my mistake in escaping? What is the true form?

<li><?php esc_html( '<a href="#"> HOME </a>' ); ?>xx</li>

The point of esc_html() is to prevent any HMTL in the value from being interpreted as HTML. There is nothing in this example that needs to be escaped. If the link URL was a variable, that would need to be escaped.