What part of this indicates a possesive? How do i know its "my" house?
When people refer to their own house they almost never use the possessive. So if they're talking about a house, and don't indicate if it's someone else's, it's certainly theirs.
"para casa" and "em casa" are idioms implying one's home.
You can translate both by "home", which also implies a possessive.
Also, then how do you simply just say "I walk to the house" in a way that differentiates it from saying "I walk to my house" ?]
'The house' would be 'a casa'. (...para a casa) I think. But like you, I am still learning.
The fact that I walk to the house does not mean it is my house
"Para casa" = my house/home
"Para a casa" = to the house
You're right! Although this association is not wrong, it is not a rule. It will always depend on a context. The only way that unquestionably refers to my house, is when there is the use Minha.
Eu vou a minha casa?
Eu vou à minha casa ( com À).
Deveria aceitar: I walk to home, já que não há obrigatoriedade de se estar referindo à própria casa.
Not always "Eu ando para casa" will mean that the referred house is mine, will depend on a context.
Should be accepted: I walk to house.
"I walk home." I find this a reasonable translation. It's the way I would most commonly express the same idea.