Why am I getting 'deprecated' errors and potential PHP security vulnerabilities with free scripts?

Hey everyone! I'm super new to the whole self-hosting scene and have been trying to get my first little project off the ground. After reading some posts here about the difficulties with finding reliable free PHP scripts, especially outdated ones, I decided to dive in and try a few for a simple contact form and a small gallery.

However, I'm consistently running into these 'Deprecated' warnings during installation or initial setup, and sometimes even explicit 'Security Warning' notices. It's really confusing for a beginner like me, and I'm not sure if I should be concerned, especially regarding overall php script security for my server.

Here's an example of what I'm seeing in my error logs:

[10-Oct-2023 14:35:01 Europe/London] PHP Deprecated:  Function eregi() is deprecated in /var/www/html/script/index.php on line 45
[10-Oct-2023 14:35:01 Europe/London] PHP Warning:  "mysql_connect" is deprecated and will be removed in a future PHP version in /var/www/html/script/db_connect.php on line 12

Could anyone help me understand what these 'Deprecated' errors actually mean? Is it generally safe for a beginner to just ignore them for a small, non-critical project, or do they always signal a deeper issue? More importantly, how can I identify actual php script security vulnerabilities in older free scripts? What are the best practices for finding more reliable and secure free PHP scripts nowadays, especially if I'm trying to avoid these kinds of warnings? Are there specific places or criteria I should be looking for?

Thanks in advance for any guidance you can offer!