Checkout page changed colour.

My style suggestion didn’t work because the relevant file: wp-custom-css.css contains parse errors preventing it from being read. Maybe this file was edited recently.

The syntax for comments in css files is:

/* this is a valid comment */
/* so is
this */
///// but this causes a parse error

To check for other errors, you can validate your custom css using this service:
http://jigsaw.w3.org/css-validator/#validate_by_input

wp-custom-css.css is still showing the //// in some places so not validating. I can’t really examine it as it is. Once there is a parse error, some things might work and some won’t, its no-mans land.

I see that you have removed all your custom css except my snippet from above. That wasn’t my intention, only that you should reformat the //// lines. I didn’t study the other snippets but if you can bring them back they may have the cart items frame css.

The little arrows are still there, only they are just not visible until the field has hover. To remove them use:

input[type=number]::-webkit-inner-spin-button,
input[type=number]::-webkit-outer-spin-button
{-webkit-appearance:none; -moz-appearance:none; appearance:none; margin:0}

To make the text colour readable in the quantity box and in the checkout boxes, use:

input {color:#afafaf}

Your theme’s stylesheet says your theme is intended for WordPress 3.2.X (and you have 4.3.1) so consider asking the supplier if they have a theme update.

Generally sites that don’t get updated seem to have more problems than those that do, though some here would disagree…

To get all the inputs looking alike, try:

input[type="text"], input[type="email"], input[type="tel"] {padding:8px 9px; color:#afafaf}
.select2-chosen {padding:4px 9px; color:#afafaf}

Persevere with the updates or your site will eventually have problems and may have security vulnerabilities which would otherwise be patched.

On my site, after PayPal, you come to the “thank you” page, then to get to the download link you would go to the “My-account” page. Generally its possible to add bits of text using a hook:
https://docs.woothemes.com/wc-apidocs/hook-docs.html
but to alter text you would probably have to make a new page template. Start with this file:
/wp-content/plugins/woocommerce/templates/my-account/my-downloads.php
and put your custom version at:
/wp-content/themes/my-theme-name/woocommerce/my-account/my-downloads.php

If your theme already has its own version, start with that and make a child theme for your custom version.

PHP skills will be needed.

Regarding the button, without buying something I can’t see it. On my site its a text link, so your button is probably theme specific. You’ll need to try browser tools:
https://developer.chrome.com/devtools
Alternatively your theme’s support service may be able to help.