It's the nominative indefinite ending, -un, which is rarely written, but if it were, it would be written as زوجٌ

Notice how the small symbol above the ج looks like two small وو linked together. The grammar behind when we use what when talking about indefinite things is a bit too involved to explain here, so what I suggest you do is pay really close attention to what you hear while following the Arabic letters with your eyes, and you'll eventually get a feel of what to use when. It takes a long time to acquire this skill, so just be patient and listen to a lot of Arabic while following text every day. You'll get there eventually :-)

PS: We also often drop the sound when reading out loud, so don't worry too much about it.

Nope, in Arabic, جديد only means "new" and not "young." It can mean both a new husband as in somebody that a divorcé(e) has gotten married to, or somebody who has just become a husband.