A different thought: if each of these lines is set up in a similar way (with tabs separating each section), then you should consider one of two different options, which don’t involve GREP:

• You could just select the paragraphs and convert them into a table. The rule is: If you’re making something that looks kind of like a table, and smells like a table, then it probably should be a table! :-)
• You could use nested styles… just make character styles, and then apply them using nested styles rules to each section using the “up to” tab rule. Here’s a silly example of nested styles, but it gives the basic idea: https://creativepro.com/holiday-text-fx-part-3-fun-with-nested-styles.php

No, InDesign doesn’t have a way to say “put a stroke between cells, but not if it’s at the bottom or top of a column”
I believe you would have to modify that manually, with cell styles or just selecting those rows and changing the stroke.
Note that if you change the stroke at the bottom of one page, it will also change at the top of the next column/page (because technically that border is the same).

The best way to do that is to use a font for the numbers that looks like that (with circles around them). I can be done otherwise, but it’s a bit of a hassle.
Other numbering tips: https://creativepro.com/formatting-tips-bullets-numbered-lists.php

I have to agree with you that table formatting — and especially how it relates to styles — can be very annoying in InDesign!

In this case, I would suggest not using cell styles. Rather, I think you can get everything you want with just a table style. For example, this is done with just a table definition, no cell styles:

How? Download this IDML file, open it in InDesign, and look at the table style (or the table options dialog box). Let me know if you have any questions.

I’ll have to write this up as a blog post so others can follow along…

The Customize Control Panel feature is not in the Preferences dialog box. In CC2015 and earlier it is inside the little Control panel menu (tiny little menu in the far-right side of the Control panel). In CC2017 they moved it into a new “gear” icon on the right side of the Control panel. Try turning off the cell and table styles checkboxes and see if that helps.

It’s possible that your screen isn’t wide enough. In recent versions of InDesign, they’ve added space around the widgets in the Control panel, so less fits in the width. You can adjust what shows up by making the screen wider or using the Customize Control Panel widget to hide lesser-used control widgets.