Eines Tages nahm ich esihn nicht (mit) und es hat angefangen zu regnen. Eines Tages nahm ich ihn nicht (mit) und es hat angefangen zu regnen.

This is a bit tricky. Using 'nahm/nehmen' here actually requires two fixes to make it grammatically correct. First, since you are referring to the umbrella (Der Regenschirm), you need a masculine pronoun. 'Es' is only used for neuter nouns, so we need to use 'ihn'. Second, because the verb is 'mitnehmen' (to take along), you can't forget the prefix! So it would have to be: 'Eines Tages nahm ich ihn nicht mit.' However, there is another way to write that sentence, using the word 'tat' (tun) instead of 'nahm'. This works beautifully because 'tat' refers to the action of 'taking the umbrella' instead of the umbrella itself. Since an action is neutral, the pronoun 'es' suddenly works again! The sentence would then be: 'Eines Tages tat ich es nicht und es hat angefangen zu regnen.' In essence, both sentences mean exactly the same thing. There is just a little nuance: using 'tat' emphasizes the action you failed to do, rather than focusing on the specific physical object you left behind."