Help with this error.
 

Whenever someone proceeds to registration, this is the error that it gives them:

https://vborg.vbsupport.ru/external/2014/11/24.png

This is the code
https://vborg.vbsupport.ru/external/2014/11/25.png

I do not know if that's the right file, because I cannot find anything else but what else can I do?

You need to upload all the files that came with Spam O Matic

When you see "eval()"d code on line xxx" at the end of an error message it means the error is in a plugin (line 10 of the plugin in this case). The hook on line 347 of register.php is "register_addmember_process". So you have a product that uses that location and you should be able to find it in the Plugin Manager.

The product is supposed to use a custom file called functions_ghsom.php in the includes folder but apparently it's not there

Correct, it is from the [GlowHost] Spam-O-Matic - Spam Firewall stops forum spam Mod

That is why I sad to load all the files that came with the mod. :)

Do you mean reinstall it into the host files and the Admin CP? Or what?

Just the files from the [GlowHost] Spam-O-Matic - Spam Firewall stops forum spam mod, as your site is looking for those files and can't find them.

I disabled the product for the time being and tested it, registration worked. However, now, when I log in or when people registers, it'll continue to show them as not logged in. Why is this happening? Could it just be that I have to delete my browser's cache/cookies?

Do you allow users to login to your site via both http://www.yoursite.com and just http://yoursite.com? If so, then you MUST have your cookie domain (AdminCP > Settings > Options > Cookies and HTTP Header Options > Cookie Domain) set to ".yoursite.com" (no quotes, but note the period at the beginning) or your users will have problems. Also, make sure to tell your users to click the Remember Me button when they login. You will probably need to clear your browser cookies after making this change.

I mean what I am asking is should I do a fresh install: Installing files from the FTP and the ACP, or just the ACP or what?

I am not sure. I thought they could login it from both? How would I check?

The error means that you did not load all the files that came with the mod to your server. So you need to ensure you loaded the files to the correct place.

If you still get the error after doing so, you will need to post in the mod's thread to get help with the mod. :)