I would like to offer the ability for users to open a form built using PHP/HTML and then on that form have a box which allows them to search for employees then want to send the form to without having to submit the form at this stage.
They will get a search box which allows them to enter the name or part name, the query then finds all employees which match the input string and they then choose the correct employee and that respondent is added to a list and they then search for the next employee and so on until they have added as few or many as they like.
Once they have selected the names, they then fill in some other standard fields on the form and then a separate entry is created in the “forms” table for each request sent.
Happy how to do the last part in terms of entering it into the database etc and how to do a “normal” search in PHP/MySQL but what should I do for the search within a form and add to the list pre submitting?
the technique you are looking for is AJAX which uses javascript to examine the form field as they type, talk to the php, get data, then show it back to the user without having to reload the page or sumbit the form. The exact thing you describe is called auto complete which there are many prebuilt tools for (or you can build your own custom one with some js knowledge). I am not going to try to post all the code here since it would be rather long and involved but if you search around these terms you will surely find what you need.