Assign responsible for something

Early and earlier (and also late/later) can all be used as adjectives, but whilst earlier and later are usually used to describe the relative occurance of an event to another (perhaps implied) event, early and late are used to describe the absolute occurance of an event on a (often implied) timeline.

For example, when considering a collection of paintings:

This is a nice painting, but I prefer your earlier paintings

This statement states that the author prefers paintings that were created before the current painting. This contrasts with the statement:

This is a nice painting, but I prefer your early paintings

This statement on the other hand states that the author prefers paintings that were painted early on the unspecified but implied timeline of the artist's entire career.

Similarly, suppose the theatre has showings at 8 AM, 11 AM, 2:00 PM, 5 PM, 10PM, 11 PM and midnight. Then

I wasn't able to get tickets for the 11PM showing, but I got tickets for a later showing

In this case, the tickets procured must be for the midnight showing, since this is the only showing that is later than 11PM.

On the other hand,

I wasn't able to get the tickets for the 11PM showing, but I got tickets for a late showing

In this case, the first clause is merely descriptive; tickets could not be obtained for the 11PM showing. The second clause stands alone stating that tickets could be obtained for a late showing, and hence the tickets might be for the midnight one OR the 10PM showing, since both are objectively "late showings". The 10PM showing is a late showing even though it is earlier than the 11PM showing.

When no separate comparative event is provided earlier and later mean the same as early and late, but are just less idiomatic; assuming no other context, the following two sentences are equivalent:

I prefer Mozart's earlier works

I prefer Mozart's early works (preferable)

Be aware that late as an adjective also has the meaning dead that the adjective later does not have:

The late Oscar Wilde was a very witty man.

(X) The later Oscar Wilde was a very witty man

And finally there are certain idioms where the choice of "late/later" and "early/earlier" is fixed. In these cases, you should not substitute late for later or early for earlier (or vv):

The early bird catches the worm!

(X) The earlier bird catches the worm!

Yes, you can say it if you wish but it would be misleading unless someone had assigned you to be a taxi driver, which would be most unlikely.

A job is a description of any kind of work a person or organisation undertakes, whether paid or unpaid.

An assignment is of its nature usually a temporary function/commission/appointment in which somebody is sent to do a particular job for a time.

If you are for example an accountant, you can be assigned to a particular desk or account; a policeman to a particular investigation, a soldier to a particular unit, a banker to a particular branch - and so on.

In all these cases, somebody senior assigns someone more junior to do the job.

So, in your example, the journalist undertook a particular job in China to either report on or investigate or follow up a story.