"The firm where I will be working has offices in Russia".

Currently I'm a bit stuck with how to express this and I have to do it in two chunks:

Фирма где я буду работать [PAUSE] ... у её офисы в Россию.

Can I do:

У фирмы где я буду работать офисы в Россию ...
Remember that after prepositions, её and его mean "her" and "his", respectively.
When a third person pronoun is *itself* the object of the preposition, it gets an initial н!

(У неё) ... . - At her -- this one is a complete package, it is a finished prepositional phrase
(У её ...) ... . - At her (blank) -- this one still requires a noun to act as the prepositional object

Horrible example because English has the problem that Russian is avoiding here xD

У него - at him
У его друга - at HIS friend

Also,
в + prepositional - location, in
в + accusative - destination, into

So "в Россию" indicates movement into Russia, rather than location.

Previous suggestion is probably best, but another alternative could be
Компания, в чём я работаю, имеет офисы в России.

Note that whenever a noun is getting an inset description, mostly starting with question words что кто где etc., both sides get marked with a comma so that the reader knows when "we're back on the main road", so to speak.
This is important for maintaining the free word order system.
These inset mini sentences are called subordinate clauses (because if you shave off the rest of the sentence it won't make its own sentence)

Компания, в чём я работаю, имеет офисы в России.