1. The online status field is displayed in the Main view in "Group summary" and "General information" sections. But these are on-screen reports that are build at some moment from the data that is actual by that moment. There is no particular way for them to refresh on their own. The same problem would be in Table reports if you include the Online state field there. It will not be refreshed automatically until you rebuild the report.
The ever-actual online status is displayed by the indicators of the "Online status" assistant that you see in the network tree next to each asset.
We could try and add some hack that will force the field in the Main view to refresh automatically if you consider this important (but even then it won't work for printable reports in "Viewer & reports", or for "Table reports" (both on-screen and printable), only for the view that is on your screenshots). Please let us know.
Also, do those online status indicators in the network tree work correctly for you? We've had some reports that they showed incorrect information sometimes.
2. TNI pings assets each 60 seconds, but each asset is re-pinged not earlier than X seconds pass since it was last pinged (where X = number of assets, with a minimum of 60 seconds, and maximum of 10 minutes). These parameters cannot be changed via Options. So in case of 129 assets all assets are re-pinged each 2-3 minutes.
3. Considering the above, there is no sense to specify last ping time next to the "Online status" assistant name, as it will always be "not more than 1 minute ago". However, it would be interesting to specify last ping time in the hint of the indicator for each asset specifically.
P.S. Thanks for your positive feedback.