In my experience, it is not unusual to have to reapply styles to table cells.
I would agree with Peter. That's been my experience as well.
If you are applying style to table text, it should pick up all the styles that you have selected. If it is not, then it is likely that there are rogue character styles or manual formatting still applied to the text.
Select some of the text and look at your paragraph style panel. If it shos a "+" next to the name of the style, then there are other elements conflicting with the style. You can fix this by selecting the text and/or cells with the text, and Right click on the paragraph style. From the contextual menu, select :apply style and clear overrides".
This should clear out any manual formatting overrides. If the problem persists, you can select the option to clear overrides and character styles.
As for linking the tables in InDesign and Excel, it IS possible, but you have to ensure that the styles in your InDesign file are named identical to the styles in the Excel file... If they are not, then whenever you update the Excel file and then refresh the link in InDesign, all your text styles will change (where the names do not match).
PS: I have used preformatted tables in InDesign with paragraph styles applied and pasted data from Excel into them without issue and without having to reapply styles to the table cells.