How to validate my form

$table = wp_save;

This is setting $table to a PHP constant wp_save. If I had to guess I’d say you don’t actually have a constant by that name, and just meant to set the table name to wp_save. To do that you need to put the table name between quotes, so that it’s a String:

$table="wp_save";

However, given that WordPress users can change the wp_ prefix in the database to whatever they like, you should use $wpdb->prefix to use the correct prefix as set by the user:

$table = $wpdb->prefix . 'save';

Before diving in too deep on building a plugin though, I’d suggest brushing up on the basics of PHP so that you know the difference between the different types of values, like Strings and Constants. Ultimately everything you’re going to be doing in the back-end is PHP, and the fundamentals don’t differ just because it’s WordPress.