To bring part properties into the drawing, a note with the $PRPSHEET:"property name" is added. Quotes are required.
For notes, there are menu buttons and dialogs to select from.
To add this to a general table, you must type the text literally.
You can also add it to the BOM by inserting a new column, select custom property as the type, then select the property name.
If you only want the data to be on some part drawings and not others, then create a general table and save it as a template.
Then insert a general table, using this template, for those particular drawings.
For assemblies, I'd go with the extra BOM column.
I would create a "New" BOM template then when you want to show the above information then just add that BOM
You can insert this information in a table, but it will need to be structured differently than your example. You're showing a row for each property, but I assume a column for each property would be okay? Insert a drawing view of your Part, then click on it to highlight it and insert a Bill of Materials. You can assign whatever property you want for each column by clicking on the blue box at top and choosing the "Link to Properties" icon. Add columns as needed by right-clicking in the same place and choosing "Insert >Column Right (or Left)" from the drop-down.
You can also link Notes to Part Properties. Attach a note leader to the Part and choose the "Link to Property" icon in the Note's PropertyManager. There will be several options and drop-downs in the resulting dialog box, and they've changed between SW2015 and SW2016, but you should be able to figure it out.
As a related topic, look into Tab Builder for entering your data.
It's usage wasn't stated either way in your OP, but I'd just thought I'd mention JIC.
This should be easier to do, you should be able to add a custom property to a general table but it looks like that does not work. To add another issue happening in my case I want to pull in a a custom property from a specific configuration. I have multiple configurations and want to show the dimension that is changing in order to make a table drawing. I would be nice to not have to key in every time. I'm not sure this is possible as the bom table is pulling info from the active config only in the drawing view I used.
I submitted this feature request for many of the missing tools we need for making tabulated drawings from configurations. I think it relates to this thread. Please review and vote on it by logging into your Solidworks Customer Support Portal and searching for the number above.