If I multiclass into Paladin, can I use up any class’s spell slots for Divine Smite?

Divine Smite: Starting at 2nd level, when you hit a creature with a melee weapon attack, you can expend one paladin spell slot to deal radiant damage to the target, in addition to the weapon’s damage.

I’m multiclassing into Paladin/Warlock/Sorc, and I’m wondering: can Divine Smite only be used in spell slots gained specifically by taking a level in Paladin, or can all available spell slots be used?

RAW is it against the rules to take another class’s class feature as a feat?

For example, I want to play a Firbolg life cleric (because our party desperately needs more healing) but for roleplay purposes I don’t want him to wear armor so I was thinking that I could take the Unarmored Defense Feat and use my Wisdom like a monk. So imagine my surprise when I found out that it wasn’t a feat and just a class feature of some classes. Thus my question.

My DM is pretty is pretty lenient so as long as the rules don’t specifically say “This is forbidden” she’ll probably let me do it. Now I know that this could be easily solved by just taking 1 level in monk so that’s an option but not my first.

There is an extremely related question, Gaining Other Class Feats, but that doesn’t answer my “Is it explicitly forbidden?” question.

Other related questions (both from 3.5):

Is choosing a different class feature too good as a (house rule) replacement for a redundant feat? Answer seems to be “No, that is a fine rule.”

What can I do with an existing feat that I later get free as a class feature? Answer is “Retrain the feat for a new one.”

Are there any spells that aren’t on any class’s spell list?

Chapter 11 of the 5e Player’s Handbook has a list of spells each spellcasting class can learn, followed by a description of all the spells in the game.

I am wondering: are there any spells that are described in the second part of the chapter that aren’t in any class spell list in the first part of the chapter?

I am thinking those could be spells only learned by certain class or race features, or spells added to the spell list by sub classes. They could also just be spells described but not mentioned anywhere else in the book, for whatever reason.

My questions regards the PHB primarily. But I would also by interested in knowing if this is the case for any of the supplementary books, that add new spells, like XGtE.

Can a multiclassed Spell Sage (wizard archtype) use the ability Focused Spells with a different class’s spells?

Can a multiclassed Spell Sage (wizard archtype) use the ability Focused Spells with a different class’s spells?

The ability says:

once per day the spell sage’s understanding of spells allows him to increase his caster level by 4 for a single spell cast.

Can this be applied to a sorcerer’s magic missile?

Can a class take a different class’s spell in their ritual book?

If I am a warlock and I take the Ritual Caster feat, can I take spells from a different class and put it into my ritual casting book?

The feat says:

When you choose this feat, you acquire a ritual book holding two 1st-level spells of your choice. Choose one of the following classes: bard, cleric, druid, sorcerer, warlock, or wizard. You must choose your spells from that class’s spell list, and the spells you choose must have the ritual tag. The class you choose also determines your spellcasting ability for these spells: Charisma for bard, sorcerer, or warlock; Wisdom for cleric or druid; or Intelligence for wizard.”

So, as a warlock, can the two I select be from that of a sorcerer?