A bit hard to to with a table.
A far more easy way to approach it would be to use a normal textbox, if possible, and add lines later (if required). Horisontal lines (lines or fill behind paragraph) can be added in paragraph styles and vertical lines (lines or row color marker behind text) can be drawn.
My InDesign is not in English so bear with me if some inaccuracies
- Make paragraph style and character styles (for the columns planned to be different)
- Use "Nested Styles" found under "Drop caps and Nested styles" in the "Paragraph Style Options"dialogue (edit paragraph style).
- Make adjustments as needed.
For rows - this one took years for me to figure out - but are quite simple and a real time saver if long tables:
- Make two paragraph styles (for even and odd lines).
- In each of them set the other style as "next paragraph style".
- Select all paragraphs in your table
- Give them the style of the first paragraph style
- Right click the paragraph style (in the Paragraph Style window) and choose "Apply "style 1", then Next style"