For the first point: Power BI can read data from a SQL table and present it. OOB you could use the KPI visual and set up the Target goals so the text changes to red when "data issues" exceed a tolerable count. There are alternative visuals that might suit in the Custom Visuals Gallery e.g. Synoptic Panel, Table Heatmap.
For the 2nd point: This level of control of tooltips isnt available AFAIK. I would add a Table or Long Text (Custom Visual) and shrink the height to a single line, perhaps at the bottom of the page. The data table fed in would be rows of data issues, with a default single row showing "No current data issues". If there were "data issues", I would set up the dataset so the first row shows something like "NNN data issues detected - click Focus mode to review". When the user clicks "Focus mode" on that vis it will zoom up to full screen and show all the rows of data fed in, with a scroll bar if necessary. This is probably more practical functionality than a tooltip.
