Is a <form> valid over a ?

Answer 1

It's not valid. I'm guessing you want to remove the default padding of the form element. This is better done through CSS:

form {
    padding:0;
    margin:0;
}

or

Your approach used to be very common to remove the default form padding (before CSS became popular). Now you should put the form tags outside the table. Preferrably you shouldn't even use a table here, but that's not the question, so I'll let it slide. ;)