Hello,
To redirect your vendors to the dashboard when logging in, for WC Vendors free, put this code in your theme/child theme functions.php file:
https://gist.github.com/fervous/feb3a043c399b0b1fb18f9488e75aed8
For the second question– you need to add some css to those links since your theme does not have the “button” class that many woocommerce themes do.
Try something like this in your theme/child theme style.css file — you can, of course, change or add more css if you wish:
a.button {
margin-right: 4px;
border: 1px solid #ccc;
padding: 4px 6px;
}