The Turn Co-ordinator is generally electrically operated, so is not affected by a suction pump failure.
The Attitude Indicator and the Direction Indicator ARE powered by the suction pump. Both of these instruments will fail if the pump fails. The gyros in these instruments have an extremely fast average spin rate of about 18,000 rpm. When the pump fails, the gyros will start to slow over a period of time, causing the instrument to show gradual errors rather than a sudden break-down immediately.
What checks should be performed on your aircraft for the first flight of the day when it contains 100LL AVGAS?
Check the colour is Blue, and that no debris is floating or has collected at the bottom of the fuel tester, and check the fuel smells like AVGAS and evaporates readily
When the alternate static source is selected, the static source is opened to internal cockpit pressure (obviously this type of alternate static source is only used in unpressurised aircraft).
Contrary to what you might think cockpit atmospheric pressure is actually slightly LOWER than ambient “outside” pressure. This is because more air gets “sucked out of the cockpit” than goes in!