Hello,
1- As you know the Page Title Bar is globally set under the Theme Settings > Page Title Bar but for the Category pages, you can specifically define the Image for Category Page Title by editing it: https://snipboard.io/KwMTb7.jpg
Further, you can control the the Page Title Bar size under the Theme Settings > Page Title Bar too which adjust the overall Size of it: https://snipboard.io/v1f59h.jpg
Now, right now you haven’t had any Image uploaded on the Page Title Bars so we are unable to check this correctly on your Site and provide you the CSS for that (if applicable).
2- Could you please elaborate your concern more with some useful Screenshots as to exactly where you want to have Border around Text?
Best Regards