Is spellcasting not an ability?

The idea of a ‘group check’ is in the rules anywhere in 5e, or is your homebrew rule?

Watching the PAX D&D game. The idea of a ‘group check’ where it’s a matter of more successes than failures, is that in the rules anywhere in 5e, or is that your homebrew rule?

Why Forge cleric does not gain martial weapon proficiency, but is able to use Blessing of the Forge on a martial weapon?

Druid’s Wild Shape, it says you “retain any abilities given by your class/race” : could I still use psionic powers?

Does Falling in Love use up your movement?