Model validation in regression

I was wondering, for this question and why. I think its in-sample but curious why.

1) Models need to be validated:

a. In-sample

b. Out-of-sample

c. Both in-sample and out-of-sample

Also, for heterosketadicity (below), I got d) a non-linear pattern but curious why.

2) Heteroscedasticity can be detected graphically by plotting the residuals against the in-sample predicted value Y-hat by visualizing these shapes:

a. a tube

b. a funnel

c. a double bow

d. a nonlinear pattern

e. a funnel, a double bow, or any nonlinear pattern
I'm taking a linear regression class at Cal and stuck. I would appreciate if you would be able to explain the quesions above, since my book didn't really cover it well.