Regarding your main question, the meaning of "jealous" in Exodus 34:14 pertains to worshipping God to the exclusion of all others.
God will not put up with rivalry or unfaithfulness. Usually his "jealousy" conerns Israel and assumes the covenant relationship [analogous to marriage' and the Lord's exclusive right to possess Israel and to claim her love and allegiance. Source: NIV Study Bible notes on Exodus 20:5).
As to your secondary question, God is not so insecure that he needs to know how much we love him.
What happened to Job is a reminder that we are not privy to God's thoughts and neither do we understand the "cosmic conflict" that is going on the behind the scenes. This morning I had to respond to a question about suffering and untimely death, and I found an article on a Protestant web site that addresses the issues you raise, part of which sums it up thus:
The Book of Job teaches us to trust God under all circumstances. We must trust God, not only WHEN we do not understand, but BECAUSE we do not understand. The psalmist tells us, “As for God, His way is perfect” (Psalm 18:30). If God’s ways are “perfect,” then we can trust that whatever He does—and whatever He allows—is also perfect. This may not seem possible to us, but our minds are not God’s mind. It is true that we can’t expect to understand His mind perfectly, as He reminds us, “For my thoughts are not your thoughts, neither are your ways my ways, says the LORD. For as the heavens are higher than the earth, so are my ways higher than your ways and my thoughts than your thoughts” (Isaiah 55:8-9). Nevertheless, our responsibility to God is to obey Him, to trust Him and to submit to His will, whether we understand it or not. Source: https://www.gotquestions.org/Book-of-Job.html