1) WooCommerce adds a body class to pages it’s active on, knowing this you would then use this CSS:
.header-right.col-sm-4 {
display: none;
}
.woocommerce .header-right.col-sm-4 {
display: block;
}
2) You would need to manually add those to your mobile menu as sub items. You can hide them from the menu using:
#mobile-menu ul.alt-mobile-menu {
display: none;
}
3) You would need a developer to help you with this modification. You will want to override the function sf_get_account()
within the supplied child theme.
4) Looks like you are already doing this.