I have used multiple tabgroups on a lot of sites and have never had a problem with the tabs having the same appearance, so it is unusual that you say it looks ‘off’ to have more than one set of tabs on a page with the same style.
The customiser only supports a single set of styles for all of the tab groups on a site.
You can use the customiser to build multiple sets of styles and then manually copy those styles into your child theme’s stylesheet adding extra classes to each CSS rule to target specific tabgroups, however this will double the amount of CSS to the pageload so is not really recommended. Alternatively you can use one set of CSS rules from the customiser and add a small subset of the CSS rules to your child theme stylesheet to override the defaults by making a small change – such as the tab border colour.
As this first question refers to the paid add-on it and these forums are only for providing support for the free plugins listed on www.remarpro.com, I can’t provide specific support for the customiser add-on here, I’ll be happy to provide more detailed help on this if reuqired if you send me a message via the support form for the add-on at: https://cubecolour.co.uk/tabby-responsive-tabs-customiser/tabby-responsive-tabs-customiser-support/
I’m not sure that I fully follow what you mean by entering text on the same line as the tabs in your second question. Do you mean you want to include some non-clickable text alongside the tabs and still above the tab content? If so I don’t think there’s a simple way to do this without making a customised version of the tabby responsive tabs plugin.
