Inumin is the verb root "inom" in its infinitive form. It's often used as a noun meaning any kind of beverage, or it can be used the way you wrote it in your second sample sentence. Uminom is also an infinitive form verb but focuses on the actor instead of the object, which is why it's often attached to an ang pronoun and followed by one from the ng set. Your sample sentence is different because you started with "Gusto kong..." but this conjugation is normally followed by an ang pronoun or proper noun. The rule is the same with kumain, but kainan is different. Since -an affixes indicate the location where an action is being done, kainan is usually translated as "restaurant" but can mean anywhere in general where something was, is, or will be eaten. This is done by conjugating as you would any other -an verb: kinainan = past, kinakainan = present, kakainan = future. To indicate the thing that has been, is being, or will be eaten, just conjugate kain the same as above without the -an suffix. Also, the word for cooked rice (kanin) is a contracted form of kainin, the object-focus infinitive form.

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