Does tamoxifen cause weight gain?

Yes. Tamoxifine is a first generation of designer estrogen (i.e., estrogen analogue). All estrogenic compounds may potentially increase weight, but not much. Tamixifene may increase weight of the user by approximately 1 to 2 lbs. Similar effects may also exist with the second generation estrogen agonist/antagonists analogues, such as raloxifine. Weight-gains are lesser than with estrogen compounds.
Yes. A routine of healthy diet and routine purposeful exercise is very important long term. The benefits of tamoxifen far outweigh the risks and side effects in the majority if circumstances.