Learn English – “Lived” or “have lived”

Context, context, context! Either 1 or 3 could be correct.

1 is employed in a context where your discourse concerns the time when she was living in London and mention her move to New York only to provide a 'timeframe' for her London residence; for instance:

She was living in London for several years before she moved to New York, and found British accents (once she was able to understand them) much more attractive than that of her native Minnesota.

3 is employed in a context where your discourse concerns the time when or after she moved to New York and wish to mention her prior residence in London as the source of some state which obtained at that later time; for instance:

She had lived in London for several years before she moved to New York, and found it difficult to understand even midwestern American accents when she returned.

"The Chinese invented the printer."

Statement of about the past, that this is a historical fact. (simple usage of the past tense of "invent").

"The Chinese have invented the printer."?

Saying it that way implies it just happened, like you'd say "The Chinese have invaded our moon base!". As discussed in comments, you can get away with this usage in reply to a question like "What have the Chinese invented?", because that gives a context for the statement.

I think in most cases, the meaning will still be clear whether you say "invented" or "have invented", but it will probably sound strange to native English ears if its clear from context you don't mean "just now" when you say "have invented".

edit: There are other ways to use present perfect tense that don't imply something just happened, but this specific usage does (outside of a context provided by a question, or an introduction like "Let's consider what Chinese civilization has accomplished"). See the comments on this answer for discussion.

See the other high-voted answer for an analysis of how the grammar rules apply.