because that is "(my) lubimy kanapki". they mean almost the same thing - but you learn different words :)
It is the subject, in english I is used in the subject and me after the verb
Could this phrase also be translated as "You and I, we like sandwiches." If not, why? How would I express this phrase? More like "Ty i ja, my lubimy kanapki."?
To sound naturally in Polish, it could be "Ty i ja, obaj/oboje/obie lubimy kanapki." or "Ty i ja, my obaj/oboje/obie lubimy kanapki."
In other words, "my" alone does not sound well, it requires a numeral: "both": for 2 persons: "obaj" is 2x masculine, "obie" - 2x feminine, "oboje" - mixed; also "oba/obie" would be a collective numeral for non personal nouns, like 2 animals or inanimate objects (depending on their grammatical gender).
But this type of phrase with redundant subject, does not serve to give some information about any fact related to (direct or indirect) object, but to stress the similarity between two parts making the collective subject (you and me in this case).
So just to clarify, obaj/etc. translates roughly to "both" with the purpose of indicating a connection, and the form depends on the two beings involved? So if it were two women for instance, it would be "Ty i ja, obie lubimy kanapki."?
I don't know what you mean but in Polish you would rather say either "Ty i ja lubimy kanapki" or "My lubimy kanapki". Combining both is rather ucommon but still possible.
Well, technically there is no equivalent of 'both' in the Polish sentence... but that makes a lot of sense to me. Why not, added.
We like sandwiches should be acceptable because it would be understood and uses less time to say
A (Polish) friend always uses this construction "my z tobą lubimy..." to mean "you and I like". Is it a standard construction?
That even sounds exactly like Russian. So, I did some research, but couldn't figure out whether this is an archaism or a Russicism/Ukrainism. I would even say that it's both. Famous Polish writer Juliusz Słowacki wrote in his Balladyna (written 1834) - "O! my z tobą będziemy szczęśliwi!"
This course has shown me that my own particular brand of Polish is a total hodgepodge mix of archaic, different regional slang, country bumpkin and uber- intellectual. Throw into that a sprinkling of totally fabricated words and phrases. That's what happens when the people you learn from are all expats (many emigrating after the second world war) and from all walks of life :-)
I am so happy that this sentence reads is constructed such that the English comes out correctly -- as opposed to how so many Americans today would say: "Me and you like sandwiches."