Q: What is the correct way to know if Sku Grid is monitoring my products?
A: Sku Grid will always monitor your supplier URLs assuming that the account is not on vacation mode and as long as there are supplier URLs entered into the grid. You would then receive email notifications based on supplier changes (if they meeting your settings criteria in your notifications settings).
As far as revising your items, if the supplier price or stock changes and you've waited long enough (based on your checker time in general settings, and your price/stock in your listing changed according to your settings, then everything is working fine. But it really depends on what your current set up is and what it is you want sku grid to do for you, as people use it in so many different ways.
You can also use the filters on your grid (here's a video on filters) - CLICK HERE
You can select different things such as items that have gone out of stock, in stock, etc... and then click on your listing link in the marketplace item column and see that the change has been completed.
The same with the 2nd set of filters on the page - you can select the Out of Stock Items filter and then click on your marketplace item link to see if your product was placed OOS properly or not.