"Checked fields" is a field formatted with check boxes are are you attempting to describe something else here?
Checbox groups do work in table view as long as you make the column wide enough to show all the values. You may find creating a list view will work better. (I rarely present users with a table view as some of the features available often create confusion when users resize, re-position or even remove fields from the view--all things that aren't possible in a list view.)
To tabe a contact as "do not solicit" you can simply add a field to the contact table that only stores a value for "do not solicit" contacts. This could be a number with 1 identifying the do not solicit contacts or it can be a text field that stores the text "Do not solicit". In either case it can be a single value check box field where clicking the checkbox marks the contact as "do not solicit".
I was able to solve my issues. Thanks for your answer!