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Learn PolishHi Ania, sorry for late reply.
móc means to be able to in a sense that certain conditions are met, or we are allowed do to something. A few examples:
Ja mogę zostać na dworze do 8 wieczorem. I can stay outside till 8pm.
Możesz mi pożyczyć ołówka? Can you lend me a pencil?
umieć is used to inform about certain ability, skill or knowledge. For instance
On ma tylko 5 lat i już umie czytać. He is only 5 and can read already.
Umiesz pływać? Can you swim?
Regarding verbs chodzić oraz iść, it is more complicated. Chodzić (I think) it is aspekt niedokonany in Polish grammar, it describes a process of walking somewhere, a repeted action that can happen many times:
W każdą niedzielę chodzę do kościoła. I to to church every Sunday.
Iść indicates that the action is happening now or will happen in the near future (like present continuous tense in English):
Ja teraz idę do sklepu. I'm going to the shop.
Co robisz w sobotę? Idę na basen. Where are you doing on Saturday? I'm going to the swimming pool.
I hope this helps, please let me know Ania if you have any additional questions about Polish verbs.