For the binomial GLM in R:

A possible link function is the identity

The default link function tends to its extreme values faster than the cauchit link function

A possible link function is the probit

The default link function is the logistic

A possible link function is the logistic

Link functions need to restrict the dependent variable to being non-negative

The default link function is the identity

Link functions need to restrict the dependent variable to being between zero and one

The default link function is the probit