It is better to do your homework and complete it carelessly than not to complete it.

[Jit833]

1) It is better to do your homework and complete it carelessly than not to complete it at all.
2) The key to my house is not working well because it is a duplicate one.

Are the sentences correct?

[Raymott]

1) It is better to do your homework and complete it carelessly than not to complete it at all.
2) The key to my house is not working well because it is a duplicate one.

Are the sentences correct?

They're grammatical.

[emsr2d2]

1) It is better to do your homework and complete it carelessly than not to complete it at all.
2) The key to my house is not working well because it is a duplicate one.

Are the sentences correct?

The end of #2 is grammatical but overly wordy. It can be shortened in several ways.

The key to my house is not working well because it is a duplicate key.
My house key is not working well because it is a duplicate key.
My front door key isn't working well because it's a duplicate.

In BrE, the key to the main door of your house is usually referred to as the "front door key".

[billmcd]

They're grammatical.

In addition to emsr2d2's response I would add that use of both "to do" and "complete" seems redundant to me. I would prefer:

"It is better to do your homework carelessly than not to do it at all"

But I must add that, as a teacher, I don't necessarily subscribe to that philosophy.