Are my forms a danger towards code injection?
The Short answer is yes you are vulnerable to injection. XSS to be precise which you can read more about here https://www.owasp.org/index.php/XSS_(Cross_Site_Scripting)_Prevention_Cheat_Sheet

Explaination:

All user input should be sanatized for example:

if you input &lt;script&gt;alert("This will alert");&lt;/script&gt; into your form you will notice an alert message will appear on your page

however if you sanatize the code i.e.

print "Hello, " . htmlentities($_POST['user']);


you will no longer see the alert message

using htmlentities() will help protect you from the script injection.

You would also be better validating the data that will be expected from the user

Other points which you can see here https://stackoverflow.com/questions/11554432/php-post-dynamic-variable-names-security-concerns which are based more on dynamically creating variables