Gender identification task on instance or user level?
This depends heavily on your intended use case:

When 1) is better

If you want to identify the gender as best as you can while always having access to a data set containing multiple documents/tweets then this is the way to go.

There are multiple features that you can only engineer from the full data set (like average length of tweets, tweet frequency, etc.) that might be very predictive.

When 2) is better

If however your use case is to predict the gender of user based on a single tweet (maybe even without knowing the id/origin of the tweet, only the tweet text) then you need to train a model that can make a prediction out of a single tweet.

In this case I would also encourage you to get a diversified data set which contains more tweets from several different users instead of a large class of tweets from few users.