It appears the ONLY way to gain access to spells like 'Gift of Alacrity' (when creating characters) is to turn on EGtW, Take the 'Wizard' class, and choose 'Chronurgy' as school tradition.

When Creating a Character, there are several Feats and abilities that state "you gain access to a 1st lvl Wizard spell" (for example: "Mage Initiate-Wizard") but even if you turn on access to EGtW, the spells from Chronurgy or Graviturgy are unavailable.  

I noticed when I look up spells from DnDBeyond 'Game Rules/Spells' section, they are listed. And the 'available for' tags associated with them are only 'Chronurgy' (in this example).  Where other spells are tagged with Classes ('Wizard') or Subclasses. (I am guessing this is why they don't show up)  

Is it possible to be able to select these EGtW (or other non PHB type) spells with Feats like 'Mage Initiate' if the appropriate books are set when creating characters?

Also, is there a way to adjust/augment Initiative rolls to include things like +d8 from 'GoA' or +d4 added to Investigation/Insight rolls from 'Deductive Intuition' from the 'Mark of Detection' half-elf race abilities?

Having these things already included/added to 'one click' rolls would be very helpful.  currently I have to roll then make an addition die roll and add them together, which can take more time and when sending to VTT's can be confusing to other players/DMs.

Thanks.

Quote from QAOS_ >>

It appears the ONLY way to gain access to spells like 'Gift of Alacrity' (when creating characters) is to turn on EGtW, Take the 'Wizard' class, and choose 'Chronurgy' as school tradition.

When Creating a Character, there are several Feats and abilities that state "you gain access to a 1st lvl Wizard spell" (for example: "Mage Initiate-Wizard") but even if you turn on access to EGtW, the spells from Chronurgy or Graviturgy are unavailable.  

I noticed when I look up spells from DnDBeyond 'Game Rules/Spells' section, they are listed. And the 'available for' tags associated with them are only 'Chronurgy' (in this example).  Where other spells are tagged with Classes ('Wizard') or Subclasses. (I am guessing this is why they don't show up)  

Is it possible to be able to select these EGtW (or other non PHB type) spells with Feats like 'Mage Initiate' if the appropriate books are set when creating characters?

That is correct. Chronurgy and Dunamacy spells are not Wizard spells. While most spells belong at least one class and several subclasses, Chronurgy and Dunamacy spells are the exception and do not belong to any class, but they do belong to some subclasses.

The only work around I can think of is to create a private homebrew copy of the spells and make them available to all classes, so that way you can pick them up via Magic Initiate. Ideally, Beyond can create a toggle to eliminate restrictions on spells like how they created toggles to eliminate restrictions on feats and multiclassing, but I do not think this is going to happen for spells any time soon, so the best work around now is to create a homebrew copy of the spells.

You cannot customize what individual setting toggles would include, as that would be considered homebrew, and homebrew falls under the homebrew toggle.

Quote from QAOS_ >>

Also, is there a way to adjust/augment Initiative rolls to include things like +d8 from 'GoA' or +d4 added to Investigation/Insight rolls from 'Deductive Intuition' from the 'Mark of Detection' half-elf race abilities?

Having these things already included/added to 'one click' rolls would be very helpful.  currently I have to roll then make an addition die roll and add them together, which can take more time and when sending to VTT's can be confusing to other players/DMs.

Thanks.

The dice roller is still under development, so it does not have that feature yet. If you just want to add a static modifier to initiate, you can do that via feats. But if you want to add a whole other dice to initiate though, I do not think that is possible yet. You will basically have to do what you are doing right now.

The dunamis spells aren't wizard spells, as you've observed they're Chronurgy/Graviturgy exclusive spells. As such, they are not available to any feature that grants you access to wizard spells and this is per the rules as designed by Wizards of the Coast.

As for your second query, it's not currently possible to modify initiative with dice rolls but this kind of functionality is planned at some point.

I thought "Chronugy/Graviturgy" are 'subclasses/schools" of Wizards just like "Necromancy/Evocation"... I guess I am not understanding why.  Necromancy spells are not limited to only those from Necromancy school?

Quote from QAOS_ >>

I thought "Chronugy/Graviturgy" are 'subclasses/schools" of Wizards just like "Necromancy/Evocation"... I guess I am not understanding why.  Necromancy spells are not limited to only those from Necromancy school?

There is difference between subclasses and schools of magic. One is a classification of subclass, and the other is a classification of spells. Evocation wizard is a subclass. Evocation school of magic is a classification of spells, well, by school.

Chronurgy wizards and graviturgy wizards are subclasses. Chronurgy, graviturgy, and dunamacy are NOT schools of magic (it is a separate classification system), and their spells can belong to any school of magic like evocation or transmutation.

Think of dunamacy spells more like a descriptive classification. For example, fire magic is not a school of magic, but can belong to transmutation, evocation, conjuration, etc.

Other spellcasting classes have subclass specific spell lists. While wizards as a class originally did not have subclass specific spell lists, certain wizards subclasses now do have subclass specific spell list.