The Test of Knowledge is based on the 16 rules listed at the beginning of the level. There is a blank book there, which you can drag and drop onto the rune wall, to copy them all down. One of the answers to a question is 13 (the ruin which has crumbled), but you can figure out which teleporter pad to take because that will be the only unrecognized symbol.
The teleporters to use in order are <span class='standouttext'>Spoiler : </span><span class='spoiler'>left, right, middle left then right.</span> (highlight the text to read)
The Test of Endurance is the classic chicken / grain / fox riddle, where you can only bring one across a river at a time. You can not leave the imp alone with the chest or the golum alone with the imp. This involves bringing something back to the original room temporarily.
One method; <span class='standouttext'>Spoiler : </span><span class='spoiler'>bring the imp to the next room, then return bring the golum to the second room, bring the imp back to the first room and leave him there until you get the chest to the second room, then finally go back for the imp.</span>
With the Test of Faith you will always be told that you failed. The real test how you respond.
<span class='standouttext'>Spoiler : </span><span class='spoiler'>If you take the left door to accept your 'punishment' you will pass the test. If you cheat and take the broken door meant for 'enlightened' students, you will fail.</span>
BTW, you don't need to pass these tests to proceed, but you will miss some experience and loot if you fail.