Field Affinity and Primary vs Secondary typing

Let's say I have an Appletun, a Grass/Dragon type Pokemon, and I want to put them in the field that matches their type. Should I put them in a Grass field, or a Dragon field? Will they be equally happy in either one, or does one type take priority over another when calculating affinity?

It will actually be happier in the Dragon field. Field affinity is more or less the same as gummis in the PMD series; matching type is best, field type that is super-effective against Pokemon type is good, field type that is not very effective against Pokemon type is bad, and field type that does not effect Pokemon type is very bad. For dual-types, it calculates both types' affinity and adds them. Let's say matching type is +2, good field is +1, bad field is -1, and very bad field is -3. In a Dragon-type field, your Appletun will get matching type + neutral, or 2+0 for a total of 2. In the Grass-type field, it will get matching + bad, since Dragon resists Grass, or 2-1, for a total of 1. This is also why you can't put a Normal/Ghost type in a Normal or Ghost type field, since the Pokemon's dislike of the field it is immune to is stronger than its like of a matching field. Just a fun fact. If my explanation didn't make sense, try reading this Wiki page.

Some time ago I collected some data about just how fast Pokemon gain/lose happiness in fields, and part of the result is a table on how types affect it, if you're interested: https://pokefarm.com/forum/post/5960265

I'm pretty sure it just goes by the type field it's in- If it's an appletun in a grass field, it's part grass so it's happy.

Not if the other type has a red heart on the field it has affinity to. I don't know off the top of my head regarding dragon/grass but I do know Maravol is poison/bug. Poison has a red heart in the bug field and gains no happiness there. They must go in a poison field to gain happiness.

Hmm, I put My two Alolan sandslash in ice type Field, but they don’t gain happiness :(

Because ice field has a red heart for steel and they are half steel. Try a steel field. Like I said above, you need to avoid fields with the red heart for dual types even if its a green heart for half of it.

They should still gain happiness, but slower, a steel type field would be much better. They won't gain happiness at all if they are busy, such as in the daycare, though.