the DLC is a DLC or a standalone spin-off?
It is a DLC. The base game allows you to H Kotori. The DLC allows you to H all the other heroines. The download here is the full game, and the DLC can be used with it, just know that it puts files in the data folders only.
Should I skip this version of the game and go right to the island version?
Should I finish this game first and then play the island version?
Should I install the DLC for both versions?
I find the RPG version more enjoyable, to be honest. Although, since you can use the same save folder for both, you can switch between them at your leisure. It may or may not make completing your picturebook easier if that's one of your goals. The DLC is same for both, and the exact same files. I forget whether you need to duplicate it or if both games use the same data folders.
The important information says only half the world is accessible and the rest will be available with updates, but the game is tagged as completed and no update since 2019. So... is the game complete with all the world explorable or not?
It's... completed, you can finish the game and even do a post-game boss. You can make every recipe. You can H all girls all ways. That being said, it's not 'correct'. 99% of the recipes are correct, but for some recipes, the recipe listed is not how you make the item. The recipe is duplicated, so you only get one type of item from it.
So if completion is your goal, you have to start noticing patterns of recipes. Like you do all your soups, then tomato soups, then milk soups, then ramen, then curry... but look at all the soup recipes, and if there's a bad recipe in the tomato soup group, try to do a soup recipe and replace one ingredient with a tomato. If you keep your recipes up to date as you get new items, it's not difficult if you understand that it is what you need to do.