Can taking testosterone cause weight gain or testicular atrophy?

Yes. Although weight gain can be caused by medications it is multifactorial and testosterone alone would not be the culprit. In large doses, exogenous (not from your body) testosterone will definitely shut down your brain's signal to the testis to make testosterone and this can lead to testicular atrophy.
Yes & Yes. Recent study showed taking t in excess could lead to more muscle if you exercised & ate properly compared to taking "right" amount. Regardless, taking t will shut down your pituitary (acts like your home's thermostat) function which means less signal (lh & fsh) to testes. End result, less t & sperm from testes which also shrink b/c no stimulus. Off-label options HCG or Clomiphene stimulates pituit.