So "ich" can mean both "them" (non-possessive) and "their" (possessive)?
E.g., "Ich pies"
C.f. "Widzisz ich?"
Yes ich can be - oni/one in Genitive, oni in Accusative = they (masculine personal) And their - possesive pronoun for oni/one that does not change with cases.
I had to check the word 'virile', I understand you meant masculine ;)
No, this is just a phrase and not a sentence, and any form of "swój" refers to the subject of the sentence. So if anything, it could only mean "its (own) dog", the dog belongs to itself. Which doesn't make any grammatical sense, as it's not like "I'm a modern independent dog" ;)
If you even could use it, it should be "swój" as this is the masculine singular version.
In Nominative, "swój" isn't almost used at all, and the situations when it is are outside the scope of this course - also, they're rather colloquial.
The plurals are "masculine personal" and "not masculine-personal". So while a dog is masculine, it is not a person, and therefore the right version (if it would be possible here) would be "swoje".
I think I read in the comments for another question that "je" is "them" when referring to a not-masculine group. So why is "je pies" incorrect please?