بعد ساعة لدينا اجتماع في الشركة.

Arabic often uses a time expression first to set the scene.

• بعد ساعة = time frame (After an hour / In an hour)
• لدينا = we have
• اجتماع = the thing we have (a meeting)
• في الشركة = location (in/at the company)
  So the sentence is basically: [Time] + [We have] + [Thing] + [Place].

لدينا literally means with us / in our possession, and idiomatically it means we have. It’s a common, slightly formal MSA way to express possession or scheduled items:

• لدينا اجتماع = we have a meeting
• لديهم وقت = they have time

Yes, mainly in register:

• لدينا is more formal / MSA-style (news, writing, announcements).
• عندنا is also correct in MSA but feels more everyday and is very common in dialects.
  Both can mean we have. In a workplace announcement, لدينا fits well.

Because the sentence is introducing it as a meeting (unspecified). If you mean the meeting (a specific known one), you’d say:

• بعد ساعة لدينا الاجتماع في الشركة
  or more naturally:
• بعد ساعة لدينا الاجتماع في الشركة / بعد ساعة الاجتماع في الشركة (context-dependent)

Arabic doesn’t have an indefinite article like a/an. Indefiniteness is usually shown by:

• no الـ on the noun (so اجتماع = a meeting), and optionally
• tanwīn in full vocalized text (اجتماعٌ), which is usually omitted in normal writing.

بعد is used as a time adverb/preposition meaning after. It commonly comes in an iḍāfa-like structure with the following noun:

• بعد ساعة = after an hour
• بعد يوم = after a day
  In fully vowelled grammar, the noun after it is typically in the genitive (e.g., بعدَ ساعةٍ), but case endings aren’t written in everyday text.

في literally means in, but English often uses at for workplaces. Both interpretations are fine:

• في الشركة = at the company / in the company (i.e., at the office premises)
  If you want to specify at headquarters or in the office, Arabic might say في المكتب (in the office).

Yes. الـ can be used for:

• something already known in context, or
• something treated as a known institution (e.g., the company we work for).
  In a workplace setting, الشركة naturally means the company (we’re talking about / we belong to).

A common careful reading (without full case endings) is:
baʿda sāʿa ladaynā ijtimāʿ fī ash-sharika
Notes:

• اجتماع is ijtimāʿ (the ج is j in MSA).
• في الشركة is pronounced fī ash-sharika because الـ
  • ش (a “sun letter”) causes assimilation: al-sharika → ash-sharika.

Because ش is a sun letter (حرف شمسي). With sun letters, the l sound in الـ assimilates into the next consonant:

• الشركة is written al-sharika but pronounced ash-sharika.

Yes. Arabic word order is flexible for emphasis. For example:

• بعد ساعة في الشركة لدينا اجتماع (emphasizes location early; a bit heavier style)
• لدينا اجتماع في الشركة بعد ساعة (more like English order; still fine)
  The original بعد ساعة لدينا اجتماع في الشركة sounds very natural as an announcement.

You can keep the same structure:

• بعد ساعتين لدينا اجتماع في الشركة = in/after two hours we have a meeting at the company
  (ساعتين is the dual form for two hours.)

You can add an explicit pronoun for emphasis:

• بعد ساعة لدينا نحن اجتماع في الشركة
  or, more naturally, restructure:
• نحن لدينا اجتماع في الشركة بعد ساعة
  The pronoun نحن isn’t usually needed unless you’re contrasting we with someone else.