After reading the rules in the books, I still have 2 questions on very specific situations about Resistances and Immunities.
1- I have a player with the Elemental adept feat (Fire). The feat lets you ignore the resistance while dealing damage with the chosen element. Right now, we decided to "rewrite the first effect" the feat as follow : "Spells that deals damage of the chosen type ignore resistance to that element and downgrades immunity to resistance with the chosen elemental damage". We are still debating if immunity is not an upgrade type of resistance, meaning the feat was suppose to let players ignore both resistance and immunity to the chosen element. Which one of those would you apply ?
2- A character with resistance to cold damage received 6 temporary hit points from our healer. The enemy cast a spell that deals cold damage (rolling an 8). Which one of those options would you apply ?
A) Temporary hit points aren't affected by the character resistance because it represent a kind of magical shield around the target. Wich means the 8 cold damage reduce the 6 temporary hit points to zero (0). Then, since 2 cold damage remains, the target only recieve 1 point of cold damage because he's resistant to cold.
B) Temporary hit points represent a magical boost to the character stamina, upgrading temporarly its capacity to receive damage. Wich means the resistance applies to the temporary hit points. So 8 of cold damage divided by 2 because of resistance = 4. 6 temporary hit points minus 4 cold damage means 2 temporary hit points are still there.
I'm seconding filcat's answers to these questions.
D&D 5th edition is written in "casual language" as much as possible, but even if it weren't, the rules only affect what they explicitly say they affect; which means not mentioning any effect upon immunity is functionally identically to adding the phrase "Immunity is unaffected." but takes up less of the book's limited word count.
...thirding? Is that a thing? Well, I agree regardless.
Resistance and Immunity seem to rely around different magnitudes. Per the book, a character with Elemental Adaptation ignores Resistance, but not Immunity, to the chosen element. Perhaps his magic creates fire hot enough to bother creatures that live around volcanoes (ergo, resistant to fire), but no amount of heat would bother a creature that is made out of fire, for example (such as a Fire Elemental).
That said, I find nothing wrong with your houserule. It allows for elementally themed casters (Pyromancers, etc) that don't roll their eyes when they fight a Magmin.
And, for the record, while I like the Resistance/Immunity thing of 5th, I often find myself pondering monster placements. "This place deals 2 fire damage per minute. Something with Resistance still takes 1 fire damage per minute, so it couldn't live here." Sometimes I miss the difference between 5/fire, 20/fire and "immune to fire".
I will let temporary hit points being affected by resistance.
But I'll keep my house rules about elemental adept feat. Let just say I've decided that resistance and immunity are in the same category that we have called Damage Substraction (to make it different than damage reduction effects). Resistance represent a 50% damage substraction and immunity represent a 100% damage subtraction. So my house rules for elemental adept could be read as : You reduce the percentage of damage substraction with the chosen element by 50%. But I think my first wording was enough explicit that we didn't need to put numbers on the effect.
And yes, I think my houserule is better because my Wizard is a pyromancer (evocation school) and I don't want him to be frustrated against creatures that are immune to fire. This way, it lets players have great character design that doesn't impair their combat capacities too much. You can see it as if the feat where creating an upgrade version of fire (like magical infuse flames).
By the way, i've decided that dragon breath will, by default, have the effect of elemental adept. Why ? because dragons use their breath against each others in combat in the D&D lore even if they breath the same element (gold dragon VS red dragon).