Trying to understand the causes and implications of kinks in fatty acid chains I watched this video (The Deal with Fat by SciShow): 

https://www.youtube.com/watch?v=mvvx2yQRbzQ

To summarize the main points I want to discuss:


Saturated fats are chains without any double-bonds and tend to result in solid structures because they stack well.
Unsaturated fats have at least one double-bond between carbon atoms, resulting in fewer overall hydrogens. This either results in a kink (cis structure) or a straight lockout (trans) depending on whether the hydrogens around the double bond are on the same side or not. 
Kinked fats are harder to stack into lattices so they tend to be liquid, so most unsaturated fats are liquid.


My questions:


I thought there were some trans fats that were healthy / naturally occurring, such as those from certain meat products. What's the difference between the healthy natural trans fats and the trans fats made from partially hydrogenated oils and such?
What exactly causes the kink? Hydrogen atoms repelling each other?
If the hydrogens are repelling each other, then how do the chains even "stack" well in the first place if they are straight? Why wouldn't they all repel each other and remain liquid?
Why do unsaturated fats, which have one double bond and tend to be kinked, straighten out and result in solids when chilled?
No, trans fats rarely occur in nature, and are generally thought to be very unhealthy.
No, like all neutral atoms, hydrogen atoms attract each other, albeit weakly (by London Dispersion Forces). That's why neatly stacked saturated fats are solid. The kink is to do with the structure of a hydrocarbon chain; their structural formula is usually drawn as a straight line, but it's actually more of a zigzag, each carbon at an angle to the last. Loosely speaking, the double bond interrupts that, so you get one more zig than zag, resulting in a kink.
See 2.
They don't need to straighten out to become solid; they just need to attract each other enough to overcome the tendency of warm molecules to keep moving around.