Would this database work for dietary restrictions like celiac/gluten-free or dairy-free?

Yes!!! The way the guide is formatted is it has convenient food options listed within each food group so if there are any meal ideas that contain a food you want to avoid, you can swap it for anything else on the food group list that you'd like!!! The only gluten foods included are some breads/ tortillas/etc which you can totally swap for GF options & the only dairy is some yogurts & cheese, which you can also swap of DF versions!!

Could I use this guide if I'm vegan or vegetarian?

Absolutely! I've got a convenient plant based proteins section!! & in any of the meal ideas that have meat, you can swap for a plant based option using that section!