'Comer' is a verb(in it's intransitive form) that means 'to eat'. It is then conjugated based on person. In this case of 'Como' it is conjugated to the first person singular form
1.I eat. (Yo) Como 2.You eat. Tú comes 3.He/she/it eats. Él/ella/usted come 4. We eat. Nosotros comemos 5. You(all) eat. Vosotros comeis 6. They eat. Ellos/ellas/ustedes comen
Hope this helps
"Como" does not mean "eating." The Spanish participle "comiendo" means "eating."
Incidentally, Spanish gerundios are not the same part of speech as Enáglish gerunds, which can function as subjects of sentences. "Gerundio" just means the present participle ends in -ando or -iendo. Gerundios cannot function as subjects or objects of sentences.
In Spanish, if you need to use a verb as a noun you use the infinitive, as in "Comer es bueno/Eating is good." IT IS WRONG to say "Comiendo es bueno." "Comiendo" can only be used as part of a compound verb, as in "Está comiendo frijoles/He is eating beans," in which "está comiendo" is in Spanish Continuous Tense.
Spanish gerundios can also be used adjectivally, in the same way that English -ing words can be used as adjectives. For example, in "The running man never passed us," the English participial "running" acts as an adjective modifying the meaning of "man." Thus, "The horse is running/El caballo está corriendo" in a sense has the -ing/-iendo form performing as an adjective, although in this example the -ing/-iendo form is actually part of a verb phrase.
Because it is teaching you a phrase: to say that something/someone is equally [descriptive word] as someone/something else. So 'He is as nice as his father.' Or 'she is as pretty as her sister.' Or 'I am as happy as you are.' Or 'These shoes are as expensive as those hats.'
It is a useful thing to be able to say, and in Spanish they use a phrase to do so. They use the word 'tan' for the first 'as', then the descriptive word they want to compare them with, and then 'como' for the second 'as'. When they hear that pattern together, they know it always means you are saying the first thing is just as [descriptive word] as the second thing. Because that formula always has that meaning to it.
To make a sentence like this: 1, first you list the first person you are talking about (also whatever verb is needed, like es), 2, then 'tan', 3, then the descriptive thing they both have in common, 4, then 'como', 5, then the other person you are comparing them to. Can work with things or people. This article here goes more in depth, and would probably answer any questions: https://studyspanish.com/grammar/lessons/equal
My guess would be because padre is the more "formal" word, and translates to father. Papa is the informal, and translates to things like pa, papa, or dad. Although all these words are synonyms, some are more appropriate than others depending on context.
Alternatively, there's always the chance that you didn't notice a typo. It's happened to me a couple of times.
For the most part, 'su' would only mean 'your' if it was formal like with usted, etc. So if you saw 'su padre' where it was also using 'usted' or señor in the same sentence for them, it would mean 'your'. But otherwise, all uses of 'su' are usually his/her/its. And 'sus' would be the plural, so their, you all's, etc. For reference: https://www.wordreference.com/es/en/translation.asp?spen=su