God does not temp us, but allows us to be tempted for various reasons, to test us, to strengthen us, and to make us see ourselves as we are...
when you overcome a temptation, you become stronger against that temptation, and when God tests us by allowing some temptation or some misfortune, it is not for us to convince Him of anything, but to know ourselves better,
since God knows us perfectly, better than anyone including our own selves, so why would He have to test us for His own sake? God is perfect and does not need "reassuring" of any kind, so instead, we are tested for our own sake,
but temptation is not a test in itself, temptation come from 3 sources - the flesh, the world, and the devil, God allows temptation because of what good can be brought from it,
"As silver is tried by fire, and gold in the furnace: so the Lord trieth the hearts." Proverbs 17:3
if you don't know yourself, your sins, weaknesses, then you can be easily deceived by yourself and others, so it's important to learn from your falls.
God does not test us to determine our worth, He has already shown us what we're worth to Him by dieing for us on the cross,
so when He tests us, and we fall, we should never become discouraged or depressed, but instead learn from the fall, ask for forgiveness, go to confession if necessary, and resolve to do better next time.
temptation itself is not bad, although as you quoted, God cannot Himself tempt, since it is evil which tempts us, but God allows it because of what good comes from it, temptation can work in our favor whether we overcome it or not, because to overcome it we become stronger against it, and to fall gives us the opportunity to know ourselves better and improve.
and the same goes for any kind of trial, those of loss, persecution, irritations, disappointments, etc. etc.
they are good for revealing who we are to ourselves, and for keeping track of our progress,
but to answer your question simply and plainly, yes all trials comes from God, but the temptations do not, God allows evil but does not cause it, and yes when things go wrong it is a test, but not always only a test, it is also a penance for sin, either your own or anothers,
one of the best ways to understand trials and temptations, is to read the lives and writings of the saints, and the two sources i would recommend for that are www.tanbooks.com and
http://store.saintbenedict.com/index.php?page=shop.browse&category_id=12&option=com_virtuemart&Itemid=1&vmcchk=1&Itemid=1alright, hope this helps, take care.