Script Executions on index.php and admin-ajax.php

I would first ask the counter-question: What exactly do you want to achieve? Where is your pain that you want to change this?

The index.php doesn’t tell me much about WordPress. I assume you’re interested in the frontend? The admin-ajax.php is used for all AJAX requests if they don’t use their own endpoint.

I had to use plugin Heartbeat Control to disable it as i’m only allowed 800000 pm by fastcomet

why are they used for?

Unfortunately, I don’t know what you mean by “they”. So I’ll try to summarize it in general terms.

AJAX requests are used for user interactions with server-side functions. For example, when you edit a page in the block editor, many of these requests are used to provide an optimal experience for the editor.

JavaScript files are used to enable AJAX requests, but also to facilitate user interaction.

For both, the number and use depends on the functions you use in WordPress, the theme you choose and the plugins you use.

If your host restricts you in this respect, you have a choice:
a) Try to avoid AJAX requests and JavaScripts by rebuilding and using your WordPress the way your host wants you to. This can be more or less difficult depending on the theme and your way of working. Since we don’t know your project, we can’t help you with this more precisely. If you have any questions about the theme, please contact their support team.
b) Change the hoster to one without such restrictions.