As far as I understood from the Rules of D&D 5e attack spells require an attack roll against the enemy's armour class, like a normal melee or ranged attack.
Question: Against which difficulty class are heal (or other no damage spells) rolled? Or are those automatically successful and only the healing amount is rolled?
Best Answer
Spells do exactly what they say. Nothing more, nothing less.
There are a few different kind of spells, but I'm going to explain 3 basic ones and that should cover the bulk of them:
The first and most prevalent kind are the healing spells you mention. These, and most other buffing spells actually do not require an attack roll or saving throw, they simply happen. If they indicate a dice expression, you roll that and apply it the way that it says to. For instance the Healing Word spell has you roll some d4s (the number depends on the casting slot), and add your spellcasting ability modifier. You don't make an attack roll, the target doesn't make a saving throw, you just apply the healing to the target.
The second most common type of spell is a debuff or damage spell that has a saving throw attached. For this kind of spell you only roll the damage dice (if there are any), and the target(s) of the spell roll(s) a saving throw of the specified type against your spell save DC for the spell (though generally in reverse order, have the targets roll their saves first, then you roll the damage).
The third kind of spell involves an attack roll. For This you roll a d20, add your spellcasting ability modifier and proficiency bonus for that spell and then compare it to the target's AC. Then you roll any damage or apply any effects specified in the spell.
These are the 3 basic types of spells, and pretty much every spell falls into one of these three buckets. Almost all healing spells fall into the first bucket, so you'd simply roll the dice it says to roll and apply it to the target(s) of the spell. It's also important to be aware of any additional modifiers to those numbers (like the Preserve Life class feature of a Life cleric).