why not "Lubię mleko a chleb"?
Because 'a' shows contrast, and here you just name some things that you like, it should use a normal conjunction.
Lubię mleko i chleb. = I like milk and bread.
Ja lubię mleko, a ty lubisz chleb. = I like milk and you like bread.
is "ja lubie" also correct?
(Ja) lubię. Ogonek (tail) is very important. Ja is not required because we conjugate verb and that way we can deduce the pronoun. However we let them stay to underline some contradiction or the fact that this is I, who is doing it.
what is "pieczywo"?
"pieczywo" is wider than "chleb" and it includes also stuff like bread rolls and similar.
Why not Ja lubisz?
because "lubisz" is the form for 2nd person singular, not the 1st. You will learn it soon, don't worry.