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

The maximum is on all the extra radiant damage that Divine Smite adds to your normal weapon damage, necessarily including the first 2d8 (emphasis mine):

[…] you can expend one paladin spell slot to deal radiant damage to the target, in addition to the weapon's damage. The extra damage is [a variable amount], to a maximum of 5d8.

The 5d8 maximum is a limit on the extra radiant damage that Divine Smite is adding to the weapon's damage.

(For Improved Divine Smite, see the question Improved Divine Smite Differentiation.)

Yes, they stack perfectly well.

Neither ability requires an action to use, so as long as you hit with a melee weapon attack that happens to use your pact weapon you can use both. The only exception is that Eldritch Smite can only be used once per turn, while Divine Smite can be used as many times as you have melee weapon attacks.

If the intent was to use only one at a time it would be called out in the text or require a bonus action or something else that is clearly not the case here.