The Find Familiar spell is currently the only method for a wizard to obtain a familiar, and it lists the creatures available. However, a large number of creatures in the Monster Manual, such as the pseudodragon, imp, or quasit, include the 'Familiar' variant. Note that a Warlock with the Pact of the Chain feature can obtain many of these creatures as a familiar.
What you have to remember is that variant monsters, like monsters, are designed for the GM to use to make enemies more interesting. The Familiar variant is a monster variant, just like the troll's Loathsome Limbs variant or the Genie Powers variant. They're for GM use rather than player use.
The Mage NPC in Appendix B of the Monster Manual also has a Familiar variant, which says:
Any spellcaster that can cast the find familiar spell (such as an archmage or mage) is likely to have a familiar. The familiar can be one of the creatures described in the spell, (see the Player's Handbook) or some other Tiny monster, such as a crawling claw, imp, pseudodragon, or quasit.
So the Familiar variant is for GMs to create more interesting NPCs, rather than to provide players with additional options. Of course, with your GM's permission, you could obtain a more interesting familiar. This would probably involve actually finding such a creature and somehow forming a bond with it. But this relies solely on your GM to allow and arbitrate.
It's also worth considering that allowing a wizard to obtain one of these more powerful creatures somewhat invalidates the Warlock's Pact of the Chain.
The short answer is that your Order of Operations is correct for both the attack and the Fireball. The rules use the phrasing "takes damage" consistently throughout.
The example given in the Damage Resistance and Vulnerability section (page 197 of the PHB), answers a lot of your questions.
For example, a creature has
resistance to bludgeoning damage and is hit by an attack
that deals 25 bludgeoning damage. The creature is also
within a magical aura that reduces all damage by 5. The
25 damage is first reduced by 5 and then halved, so the
creature takes 10 damage.
So, the raw damage is phrased as "an attack
that deals 25 bludgeoning damage". Then all the calculations are done, then the final result is phrased "the
creature takes 10 damage". Warding Bond says that
each time it takes damage, you take the same amount of damage.
Therefore, the Cleric will take the actual amount of damage that was applied to the Paladin's hit points after all the resistances and saves were calculated.
Fireball won't change the order of operations, since the Dexterity save determines how much damage the Paladin takes. For proof, we can go to Fireball itself:
A target takes 8d6 fire
damage on a failed save, or half as much damage on a
successful one.
Or, to put it differently, a target takes half as much damage on a successful save.
Best Answer
So to start with, it's worth pointing out that you can cast Warding Bond on yourself. Touch range spells are described as:
Further, under the Targeting Yourself section, it says:
You can cast touch spells on yourself unless they specifically say you can't, and Warding Bond doesn't specify that. This is actually not a bad idea - you'll get the +1 to AC and saving throws, and the double damage you'll take will be canceled out by the resistance to damage.
Find Familiar says that:
Your familiar can deliver the spell as if it had cast the spell. This is the only way in which the familiar acts as the caster of the spell. It can certainly deliver Warding Bond for you, but you will still be the caster of the spell, and the "you" in Warding Bond will still be you, not your familiar. This is effectively equivalent to casting it on yourself directly, except that it took your familiar's reaction.