Checkout Changes

If you look at our demo website, these are already the case by default in HikaShop.
The fact that your them so close without having the "additional information" bigger is because of your template CSS styling.

You can use that CSS to fix it:
.hikashop_checkout_additional_info legend {2em;}
.hikashop_checkout_additional_info {padding-top:20px;}

I don't understand what you mean by "cart mode".

You can force a menu on checkout with the corresponding option in the config under the tab checkout. Then, in the cart module's options, you can limit its display to not display it on that page.