Is letting a plant die of thirst, when one is able to water it, considered forbidden (haram) or disliked (makruh)? And does the ruling differ if the plant is not in my home and I did not plant it, but I am able to water it?

If trees benefit the creation, then planting and watering them carries immense reward. The Prophet, peace and blessings be upon him, said: "If the Hour comes while one of you has a sapling in his hand, and if he is able to plant it before he stands up, let him do so." He also said: "No Muslim plants a tree or sows a seed from which a bird, a human, or an animal eats, but it will be charity for him." This reward continues as long as the produce of the planting is consumed, even if the planter dies.

As for wasting crops, it is reprehensible and forbidden, for it is a squandering of wealth and a destruction of cultivated land. Allah condemned those who do so in His Almighty saying: "And when he turns away [from you], he strives throughout the land to cause corruption therein and destroy crops and animals. And Allah does not like corruption." And the Prophet, peace and blessings be upon him, disliked wasting wealth.

Regarding watering a neighbor's farm, it is an act of good neighborliness, which the Lawgiver has encouraged. The Prophet, peace and blessings be upon him, said: "Whoever believes in Allah and the Last Day, let him not harm his neighbor." Many scholars have explicitly stated the obligation to give surplus water to neighbors if they request it, citing the hadith: "The Messenger of Allah, peace and blessings be upon him, forbade the selling of surplus water." As for you watering it yourself, no text has been narrated making it obligatory, but it is an act of noble character.