Is this Chinese sentence grammatical? I'm unsure about a few words and phrases
Okay .... [takes a deep breath]
就 in regard to the
BLANK1
方案 plan,
市场调查部 the Marketing Survey Department
发表了 presented their
BLANK2
建议， suggestions;
其目的为  the goal of their suggestions is
促使 to ensure that
本公司 THE COMPANY,
在相应策略上, as far as the relevant strategies are concerned
能够 is able to
与时并进， keep pace with the times
从而 and thus
提升 市场上的竞争力 increase their competitiveness in the market
BLANK 1 describes a plan which was
最近 recently
拟定 formulated
为 in order to
针对 take account of
所作出的调整 the adjustments made
在市场策略上 to marketing strategies
of/by Quest公司,
对' specificially --
以客户为主 customers as the key
以雇员为本' employees as the base,
的方案 THAT plan.
BLANK 2 describes how the suggestion includes
分 dividing the plan into
两个方面的 two parts:
内整 internal consolidation
和 and
外扩 external expansion
In answer to the other parts of the question:

Is the sentence grammatical?


This sentence should be taken outside and shot.


What does 就 mean here?


Acc. to the 教育部國語辭典 就 here is a preposition (coverb) that means: 依照。 如：「就事論事」、「就原來的規畫加以調整。」 I often translate as in regard to; this is an old habit, but surely other translations (based on?) would work too.


What does 為針對 mean here?


為 is a coverb that means in order to, 針對 is verbish creature that means to direct toward, to take into consideration. 國語辭典 gives a nice example: 「為了節省時間，請大家儘量針對問題來討論。」


What does '分内整' mean?


You've divided it wrong, its 分 | 内整 和 外扩 (两个方面)


What does '其目的为促使本公司在相应策略上能够与时并进' mean?


hopefully looking at the literal translation above will help answer