## Simple marginal effects after probit

So I have cannot find pretty much any basic information on marginal effects after probit in STATA on the net or my textbooks, so any help would be SUPER! I am running a simple probit model with both ordinal and binary dependent variables. I understand that using marginal effects can show me the impact of each variable on the dependent variable.

My questions:

1) If I run
. margins, dydx (SUPER) at (SUPER=10)
Is it correct to interpret this as showing me the marginal effect/change in Y of increasing SUPER by one unit when SUPER=10?

2)If I run
margins, dydx (SUPER)
Since the cumulative distribution function is not linear, how can there be one answer to dy/dx? Wouldn't dy/dx change as you move along the line? Or is this like an average?
Is this interpreted as 'A one unit increase in SUPER will increase Y by (generated marginal effect value)'?

3) Is it logical to interpret this the same way if the independent variable in the marginal effect is binary, or do I need to do something differently?

4) Lastly, I'm guessing this is a somewhat subjective question, but should marginal effects be analysed for all significant variables in a results chapter? Is this relevant, or just the primary dependent variable?