Consider the following model: Y=b0+b1*X1+b2*X2+b3*X1*X2, where X1 is endogenous and X2 is independent. The Instrumental Variable for X1 is Z1. How should I handle the model and compute the results?

First of all, from a gretl-specific perspective, I'm not aware of any tool in gretl that focuses on this nonlinear-in-variables IV setup.

However, on a general econometric level, this is still a model which is linear in the parameters. I'd expect the product X1*X2 to be endogenous (= correlated with the true disturbances) as well, although I believe that this is not always clear and in general I expect that it depends on the joint distribution. But if Z1 is known to be a valid instrument for X1, my pragmatic approach would be to simply compute Z1*X2 and use that as an additional instrument in a traditional linear IV setup. (I guess it would also be possible to try other nonlinear transformations of Z1, see the pretty large literature on non-linear instruments.)

If non-normal distributions are involved, another quite recent approach might be one based on (nonparametric) control functions, see this one: https://arxiv.org/abs/2207.09246 (Breitung, Mayer & Wied).

cheers

sven