Changing elements for spells

I think I remember in an older version of D&D allowing you to change a fire spell into a cold-based spell, or vice versa. In 5E, is there any way to allow you to alter say a Scorching Ray into a lightning or cold-based attack? I thought maybe sorcerer spell points might have done the trick, but I cannot find any rule that would cover it. I’m sure you could design and research a spell for that character during a downtime roleplaying option, but I was looking more for a ‘on-the-fly’ type option.

How does absorb elements work with pre-existing resistances

So I’ve looked around and can’t find an answer that quite fits what I’m wondering. For example if I were to already have fire resistance and I get hit with a red dragins fire breath would casting absorb elements halve the damage I take(effectively making it 1/4 damage) or not reduce damage at all because I already have 1 source of resistance

Does Elemental Adept ignore Absorb Elements

Scenario: A sorcerer with Elemental Adept (Fire) casts Fireball at a wizard, who uses their reaction to cast absorb elements. The wizard claims that his spell protects him and he takes half damage (or 1/4 with a successful save) while the sorcerer claims that his fire spells ignore resistance and therefore the wizard only gained an extra 1d6 fire damage on his next melee attack by casting absorb elements.

Elemental adept says

Spells you cast ignore resistance to damage of the chosen type.

While absorb elements says

The spell captures some of the incoming energy, lessening its effect on you and storing it for your next melee attack. You have resistance to the triggering damage type until the start of your next turn.

My initial read says that absorb elements gives the wizard resistance but Elemental Adept ignores resistance and therefore absorb elements would not protect the wizard from the damage of the spell at all. On the other hand, we know there isn’t any fluff text in 5e, and the Absorb Elements spell specifically says "lessening its effect on you". It can’t lessen the effect on the wizard if the wizard still takes the full damage.

So which rule is the more specific rule in this case? I think it would be Elemental Adept specifically ignoring resistance to fire and not Absorb Elements lessening the effect on the caster, but I want to know which ruling is more supported by RAW.

Does the Order of Scribes Feature Awakened Spellbook also change the damage type of Absorb Elements?

The Order of Scribes from Tasha’s Cauldron of Everything has the "Awakened Spellbook" feature. Part of the feature reads as follows:

When you cast a wizard spell with a spell slot, you can temporarily replace its damage type with a type that appears in another spell in your spellbook, which magically alters the spell’s formula for this casting only. The latter spell must be of the same level as the spell slot you expend.

Can i change the absorbing damage type of the spell "Absorb Elements"?

Absorb Elements is a spell with casting time of Reaction and an asterisk when the Reaction can take place as follows:

which you take when you take acid, cold, fire, lightning, or thunder damage

Can you replace the damage type of the trigger with that feature? That way you could absorb every type of damage with this spell. Absorbing poison, psychic, force or physical damage types.

Simplifying elements of a matrix

These elements of the matrices can be simplified by hand much further{roots can be cancelled and all}, yet the Fullsimplify in Mathematica doesn’t simply it completely.

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The matrix is:

{{-((p^2 + Sqrt[m^2 + p^2] p3 - p0 (Sqrt[m^2 + p^2] + p3))/    m), -(((p^2 + (m + Sqrt[m^2 + p^2]) (m - p0)) (-I p2 + Sqrt[       p^2 - p2^2 - p3^2]))/(m (m + Sqrt[m^2 + p^2]))), (1/(   m (m + Sqrt[m^2 + p^2])))(-p^2 p2 + Sqrt[m^2 + p^2] p0 p2 +      m (-Sqrt[m^2 + p^2] + p0) p2 - I p0 p3 Sqrt[p^2 - p2^2 - p3^2] +      I p3 Sqrt[-(m^2 + p^2) (-p^2 + p2^2 + p3^2)] +      I m^2 (I p2 + Sqrt[p^2 - p2^2 - p3^2]) +      I m (p3 Sqrt[p^2 - p2^2 - p3^2] +         Sqrt[-(m^2 + p^2) (-p^2 + p2^2 + p3^2)])), (1/(   m (m + Sqrt[m^2 + p^2])))(-I (Sqrt[m^2 + p^2] - p0) p2^2 +      I m^2 (p0 - p3) -      I p3 (p^2 + Sqrt[m^2 + p^2] p3 - p0 (Sqrt[m^2 + p^2] + p3)) +      p2 (-p0 Sqrt[p^2 - p2^2 - p3^2] +         Sqrt[-(m^2 + p^2) (-p^2 + p2^2 + p3^2)]) +      m (I (p0 - p3) (Sqrt[m^2 + p^2] + p3) +         p2 (-I p2 + Sqrt[p^2 - p2^2 - p3^2])))}, {-(((p^2 + (m + Sqrt[          m^2 + p^2]) (m - p0)) (I p2 + Sqrt[p^2 - p2^2 - p3^2]))/(    m (m + Sqrt[m^2 + p^2]))), (-p^2 + p0 (Sqrt[m^2 + p^2] - p3) +     Sqrt[m^2 + p^2] p3)/m, (1/(   m (m + Sqrt[m^2 + p^2])))(-I (Sqrt[m^2 + p^2] - p0) p2^2 +      I m^2 (p0 + p3) + I m (Sqrt[m^2 + p^2] - p3) (p0 + p3) +      I p3 (p^2 - Sqrt[m^2 + p^2] p0 - Sqrt[m^2 + p^2] p3 + p0 p3) +      p0 p2 Sqrt[p^2 - p2^2 - p3^2] -      p2 Sqrt[-(m^2 + p^2) (-p^2 + p2^2 + p3^2)] -      m p2 (I p2 + Sqrt[p^2 - p2^2 - p3^2])), (1/(   m (m + Sqrt[m^2 + p^2])))(p^2 p2 + m (Sqrt[m^2 + p^2] - p0) p2 -      Sqrt[m^2 + p^2] p0 p2 + I p0 p3 Sqrt[p^2 - p2^2 - p3^2] -      I p3 Sqrt[-(m^2 + p^2) (-p^2 + p2^2 + p3^2)] +      m^2 (p2 + I Sqrt[p^2 - p2^2 - p3^2]) +      I m (-p3 Sqrt[p^2 - p2^2 - p3^2] +         Sqrt[-(m^2 + p^2) (-p^2 + p2^2 + p3^2)]))}, {(1/(   m (m + Sqrt[m^2 + p^2])))(-p^2 p2 + Sqrt[m^2 + p^2] p0 p2 +      m (-Sqrt[m^2 + p^2] + p0) p2 + I p0 p3 Sqrt[p^2 - p2^2 - p3^2] -      I p3 Sqrt[-(m^2 + p^2) (-p^2 + p2^2 + p3^2)] +      I m^2 (I p2 + Sqrt[p^2 - p2^2 - p3^2]) +      I m (-p3 Sqrt[p^2 - p2^2 - p3^2] +         Sqrt[-(m^2 + p^2) (-p^2 + p2^2 + p3^2)])), (1/(   m (m + Sqrt[m^2 + p^2])))(I (Sqrt[m^2 + p^2] - p0) p2^2 -      I m^2 (p0 + p3) +      I p3 (-p^2 + Sqrt[m^2 + p^2] p0 + Sqrt[m^2 + p^2] p3 - p0 p3) +      p0 p2 Sqrt[p^2 - p2^2 - p3^2] -      p2 Sqrt[-(m^2 + p^2) (-p^2 + p2^2 + p3^2)] -      I m ((Sqrt[m^2 + p^2] - p3) (p0 + p3) +         p2 (-p2 - I Sqrt[p^2 - p2^2 - p3^2]))), (-p^2 +     p0 (Sqrt[m^2 + p^2] - p3) + Sqrt[m^2 + p^2] p3)/   m, ((p^2 + (m + Sqrt[m^2 + p^2]) (m - p0)) (-I p2 + Sqrt[      p^2 - p2^2 - p3^2]))/(m (m + Sqrt[m^2 + p^2]))}, {(1/(   m (m + Sqrt[m^2 + p^2])))(I (Sqrt[m^2 + p^2] - p0) p2^2 -      I m^2 (p0 - p3) +      I p3 (p^2 + Sqrt[m^2 + p^2] p3 - p0 (Sqrt[m^2 + p^2] + p3)) +      p2 (-p0 Sqrt[p^2 - p2^2 - p3^2] +         Sqrt[-(m^2 + p^2) (-p^2 + p2^2 + p3^2)]) +      m (-I (p0 - p3) (Sqrt[m^2 + p^2] + p3) +         p2 (I p2 + Sqrt[p^2 - p2^2 - p3^2]))), (1/(   m (m + Sqrt[m^2 + p^2])))(p^2 p2 + m (Sqrt[m^2 + p^2] - p0) p2 -      Sqrt[m^2 + p^2] p0 p2 - I p0 p3 Sqrt[p^2 - p2^2 - p3^2] +      I p3 Sqrt[-(m^2 + p^2) (-p^2 + p2^2 + p3^2)] +      m^2 (p2 + I Sqrt[p^2 - p2^2 - p3^2]) +      I m (p3 Sqrt[p^2 - p2^2 - p3^2] +         Sqrt[-(m^2 + p^2) (-p^2 + p2^2 + p3^2)])), ((p^2 + (m + Sqrt[         m^2 + p^2]) (m - p0)) (I p2 + Sqrt[p^2 - p2^2 - p3^2]))/(   m (m + Sqrt[m^2 + p^2])), -((    p^2 + Sqrt[m^2 + p^2] p3 - p0 (Sqrt[m^2 + p^2] + p3))/m)}} 

some of the substitution we can make are (already taken),

{p1 -> Sqrt[p^2 - p2^2 - p3^2], e -> Sqrt[p^2 + m^2]} Assuming[{Element[{p0, p, p2, p3}, Reals], m > 0}, sat2 = sat // FullSimplify] 

What more could be done to simplify the elements of the matrix?

Can absorb elements be triggered on attacks that require a saving throw or be paralyzed, incapacitated… and elemental damage on a failed save?

Say an enemy is casting a spell or using an ability that forces the player to make a saving throw or be "conditioned and take X elemental damage".

Does absorb elements go off if the save is failed? Or because of the condition effect, does that mean the reaction can’t be used if you fail the save, take damage, and conditioned? Or even can it be cast before the save (and wasted if the save passes)?