I've discussed this with a few of my DM friends, and we can't come to a solid conclusion on how it works. What can and cannot be done in an anti-magic field or zone? Example: playing out of the abyss, just starting in the slave pens that are magically warded. Could an aasimar use their radiant soul ability? Could an Eldritch Knight summon their bonded weapon? Say in an opposite circumstance, the bonded weapon being in the anti-magic field and the eldritch knight outside, could they summon it? They are somewhat specific situations, but general rules for understanding would help immensely. 

PS i guess to narrow it down, what is considered magic (racial, feature, spell, etc) and how can you tell what the source of the particular effect is (user, item, or some pocket dimension type deal, etc).

See "Is the breath weapon of a dragon magical?" in Sage Advice Compendium.

From Sage Advice:

Is the breath weapon of a dragon magical?  If you cast antimagic field, don armor of invulnerability, or use another feature of the game that protects against magical or non-magical effects, you might ask yourself, “Will this protect me against a dragon’s breath?”  The breath weapon of a typical dragon isn’t considered magical, so antimagic field won’t help you but armor of invulnerability will. 

You might be thinking, “Dragons seem pretty magical to me.”  And yes, they are extraordinary!  Their description even says they’re magical.  But our game makes a distinction between two types of magic:

• the background magic that is part of the D&D multiverse’s physics and the physiology of many D&D creatures
• the concentrated magical energy that is contained in a magic item or channeled to create a spell or other focused magical effect

In D&D, the first type of magic is part of nature.  It is no more dispellable than the wind.  A monster like a dragon exists because of that magic-enhanced nature.  The second type of magic is what the rules are concerned about.  When a rule refers to something being magical, it’s referring to that second type.  Determining whether a game feature is magical is straightforward.  Ask yourself these questions about the feature:

• Is it a magic item? 
• Is it a spell?  Or does it let you create the effects of a spell that’s mentioned in its description? 
• Is it a spell attack? 
• Is it fueled by the use of spell slots? 
• Does its description say it’s magical? 

If your answer to any of those questions is yes, the feature is magical.  Let’s look at a white dragon’s Cold Breath and ask ourselves those questions.  First, Cold Breath isn’t a magic item.  Second, its description mentions no spell.  Third, it’s not a spell attack.  Fourth, the word “magical” appears nowhere in its description.  Our conclusion: Cold Breath is not considered a magical game effect, even though we know that dragons are amazing, supernatural beings.