Thanks for posting. There's a few questions here, so I want to address them in the order that they were asked.
"How can I change the text of the groups/options that show in the optin box on the website?"
The text displayed for each of these group options will be from your list's naming conventions. So, when you refer to seeing the abbreviated versions of each group on your plugin's form, that's due to those abbreviated naming conventions being used inside of your MailChimp account, for those group's labels.
It sounds like you're looking to use the abbreviated group names in your account, but to have it display the full text on your website. To do that, you might consider using the "update list" button to your advantage.
-Update your groups in your MailChimp account to be the full text you want it to display on your website.
-Go into your MailChimp plugin settings inside of your WP Admin area and click on "Update List" at the top of the page. You should not see your website has the full text for each group.
-Now, go back to your MailChimp account and change the group names back to their abbreviated versions. You should now have abbreviated group names in your MailChimp account, but the full text for each group on your website.
"Is there anywhere I can alter the code for the plugin?"
Yes, the plugin code can be accessed by going to your WP Admin area and going to Plugins > Editor > MailChimp.
"Presently I want only the first 3 options/groups to display and want the last one WhyE hidden. How do I do that?"
The plugin will not allow you to selectively hide a single group within a set of groups. So, if for example I had a Group Titled: Foods, with sub-groups "Bananas", "Cookies", "Vegetables", I would NOT be able to hide just the "Vegetables" group. I would have to choose to hide all groups ("Bananas", "Cookies", and "Vegetables"), or none.
Alternatively, if I made "Vegetables" it's own group (separate from "Bananas" and "Cookies"), I could choose to hide that if I wanted to.
If you used the embed code, you'd have full access to the HTML code you're choosing to embed, so you could choose to selectively remove the 4th group option that you don't want to appear on your site. So, it may be worth considering using the existing embed form implementation that you have live on your site currently.
Lastly, you mentioned that though you've changed the group names in your MailChimp account, that you're still seeing the 'old' names in your plugin's form. This is likely due to that list not being updated in your plugin settings. To do that, go to your WP admin page and click Settings > MailChimp Setup. Then click on the "update list" button at the top.
If you have any further questions or if I haven't covered all topics, could you provide me with an example interaction that you'd like your subscribers to go through on your site? That'll allow me to provide my recommendations for the best implementation moving forward.