If X1 is a binary variable, s still 2SLS an appropriate method to correct for endogeneity? Would it be possible to run a two-stage probit, or the bivariate two-stage model, in Gretl?

Please be more explicit with your questions. For example, what do you mean by "two-stage probit", given that you didn't tell us your model has a binary dependent variable. Use formulas to explain what you plan or are trying to do. Then we can tell you whether (or how easily) it can be done in gretl.

thanks

sven