DigitalReadWrite_02 (helper pin=03) ... FAIL
...nothing was connected (on the Arduino 2009).
I'll just take the first Failure message:
The test sketch calls ATS_TEST_DigitalPin(2). Look at the code in the ArduinoTestSuite/ArduinoTestSuite.cpp
It sets pin 2 high and reads pin 3 if pin 3 is high then it sets pin 2 low and reads pin 3. The test fails if the value read from pin 3 is not equal to the value written to pin 2.
So...connect a jumper from pin 2 to pin 3 and try again.
To see whether other test results are significant, read the code and see if you can figure out how to explain the results and to see whether something can be done to "fix" the results. See Footnote.
Test programs are, well, programs. Sometimes there are bugs (or "issues") that causes such a program to report bugs in whatever it is testing, but which are actually bugs (or "issues") in the test program itself.
There are a couple of Failures in the ATS_StringTest
sketch that are not due to any external connections, but are actually bugs. The failures can be explained and they can be "fixed" by minor changes in the test sketch. That makes no nevermind to me, since I do not (and will not) use Arduino Strings in any of my personal programs.