Submit button inline with form fields

This should be what you need. The rules are specific to the your form ID #1. You'll want to remove the other styles you had so they don't conflict.

/* set the form wrapper to relative so we can
absolutely position inside of it */

#gform_wrapper_1 {position:relative; width:475px; float:right }

/* resize the label a bit so the text doesn't wrap &
set the line height so it centers vertically with the input */

#gform_wrapper_1 gfield_label {width:32%; line-height:2}

/* set a size for the footer container, change the
position and align it to the right of the input */

#gform_wrapper_1 .gform_footer {width:40px; height:26px position:absolute; top:-26px; right:60px;}

Test Screenshot

You may have to tweak widths, percentages, etc. further to suit your placement, but that's the general idea. Hope it helps

To answer your second question, no, you can't copy-n-paste the form HTML, it won't submit properly. It has to be displayed using either the shortcode or function call for it to work as intended.