The most common type of 5th job node is a boost node, which increases the damage dealt by your skills in earlier jobs.
For example, as a Mechanic I have the AP Salvo Plus skill as my primary bossing skill. At level 30, this hits 6 lines at 285% (followed by 350% splash damage). If I use an AP Salvo Plus boost node, I gain an additional 2% final damage per node level (plus 5% critical damage at level 20, and 20% ignore defense at level 40).
In addition to this, the 5th job skills themselves are just generally powerful and useful in their own ways.
Finally, after the 5th job advancement you have access to Arcane Symbols. Symbols give a large amount of main stat (though it isn't affected by %stat potentials) for each level. They're also the only way to deal significant damage in the Arcane River area. Here's a picture posted on the Discord earlier:
Stat distribution in Maple is incredibly simplified compared to some MMOs. Each class (except Xenon) has a main stat (which increases you damage significantly), a secondary stat (which increases your damage, but at a fraction of the amount compared to main stat), and either attack (for physical classes) or magic attack (for mages). They don't mean anything beyond that, so all you have to do is auto-assign your AP to your main stat (STR, in your case, don't put points in DEX).
In the very early days of the game, stats mattered slightly more (for example, equips used to have secondary stat requirements, like 100 STR and 50 DEX to equip something), however they were simplified in an update several years ago. So the descriptions of the stats are rather outdated and don't mean anything, at this point. Since characters can't learn skills outside of their job branch and cannot equip gear that's not for their class, there's no need to apply any points to INT or LUK.
If you've already applied points to DEX or any of the other skills, it's possible to reset your stat distribution by purchasing a reset scroll from NPC Matilda (in regular servers) or the cash shop (Reboot and regular servers). Matilda sells them for 3,000,000 mesos each (?) and I don't recall what they'd sold for in the cash shop.
Technically you can do whatever you want; you don't even have to do the quests at all, if you so wish. The only necessary quests in the game are the ones relating to job advancements, and the ones relating to 5th job (the Amnesiac Temple Keeper questline in Temple of Time).
The Alishan quest is considered rather annoying, it's recommended that you simply accept it and then leave through the portal. It does, however, give you a way to teleport to Heneseys from any town with a Dimensional Mirror, so it is somewhat useful.
The Fairy Academy quest is a theme dungeon; it does have some rather useful rewards (a low-level cape, spell traces, mesos, a low-level eye accessory).
Once you make the advancement to the warrior of your choice, you're free to travel and explore as you please, barring level restrictions. You will periodically receive story-related quests and your job-advancement quests through the lightbulb icon on the left-hand side of the screen, so you ought to keep an eye on that.