Q:

What parts, if any, of the spellcasting rules apply to Savage Sorcery? 

Codex of the Black Sun includes a focus called Savage Sorcery (p. 91), along with rules for spellcasting. 
Savage Sorcery's level 1 use is described as a "Main Action invocation".  While "Invocation" is occasionally used throughout the Codex of Dark Sun as a synonym for "Spell", it's equally used to refer specifically to the vocal part of spellcasting. 
So the question is: What parts, if any, of the "Casting Spells" rules on page 21 apply to Savage Sorcery?  Specifically:
Does it have to be declared at the beginning of the turn (and presumably would then be subject to failure on injury)? 
Can it be used in armor? 

A:

As the author of Stars Without Number:

So the question is: What parts, if any, of the "Casting Spells" rules on page 21 apply to Savage Sorcery?  Specifically:
Does it have to be declared at the beginning of the turn (and presumably would then be subject to failure on injury)? 

Level 1 can be done any time you have a Main Action available and need not be declared beforehand.  Level 2 functions exactly as normal spellcasting, except it converts the spell to direct damage. 

Can it be used in armor? 

GM's call, but I'd generally allow it, since wearing heavy armor makes it impossible to use your other spells without the Armored Technique focus, and there will be very few situations where a caster would rather wear heavy armor than have access to their spellcasting abilities.  The only generally-applicable situation is if they've run dry of spells for the day.