1) Looks like your menu.tpl and dialog.tpl files are not using boxes, so there are no boxes here. Else there is some sort of customization that needs to be carried from home.tpl to home_checkout.tpl
2) You can edit your skin1/customer/main/anonymous_checkout.tpl to modify this page.
3) There's likely a color change missing in skin1/skin1.css
4) There was no #4
5) Use {if $mode eq "checkout" AND $login eq ""}Show Text{/if}