أنا أعمل في شركة كبيرة في هذه المدينة.

You can usually drop أنا because the verb أعمل already shows “I” (1st person singular).

• With emphasis/contrast: أنا أعمل في شركة كبيرة... = I (as for me) work in a big company...
• Neutral: أعمل في شركة كبيرة في هذه المدينة. = I work in a big company in this city.

أعمل is the imperfect (non-past) form. In MSA it commonly covers:

• Habitual/regular present: I work (as a job / generally).
• Current action (depending on context): I’m working (right now).
  If you want to clearly express “right now,” you can add something like الآن (now): أعمل الآن...

أعمل comes from the root ع-م-ل related to work/do. In the imperfect verb system, the prefix often marks the person:

• أعمل = I work (prefix أ-)
• تعمل = you (m.sg.) / she works (prefix ت-)
• يعمل = he works (prefix ي-)
• نعمل = we work (prefix ن-)

Because there are two separate location phrases: 1) في شركة كبيرة = in a big company (your workplace)
2) في هذه المدينة = in this city (where that company is located)
Arabic often repeats the preposition rather than “nesting” locations without it.

It’s not an iḍāfa. It’s a normal noun + adjective phrase:

• شركة = company (noun)
• كبيرة = big/large (adjective describing the noun)

In an iḍāfa, you would have two nouns (e.g., شركةُ الاتصالاتِ = the telecommunications company).

In Arabic, adjectives usually follow the noun they describe. So:

• شركة كبيرة (noun + adjective) = a big company
  This is the standard pattern in MSA.

Because adjectives agree with the noun in gender and (usually) definiteness and case.

• شركة is feminine (many nouns ending in ـة are feminine), so “big” becomes كبيرة (feminine).
  If the noun were masculine (e.g., مكتب office), you’d say مكتب كبير.

Because مدينة (city) is feminine, so the demonstrative must match:

• Feminine “this”: هذه
• Masculine “this”: هذا
  So هذه المدينة = this city (feminine agreement).

Yes, the phrase هذه المدينة is definite because demonstratives make the noun phrase definite. In MSA it’s common to include الـ as well:

• هذه المدينة (already definite by meaning/structure)
• هذه المدينة with المدينة is the most common written form: demonstrative + definite noun.

A common fully-vowelled version is:

• أَنا أَعْمَلُ في شَرِكَةٍ كَبيرةٍ في هٰذِهِ المَدينَةِ.

Why:

• After في, the noun is genitive (majrūr): شركةٍ and المدينةِ.
• The adjective follows the noun and matches it in case: كبيرةٍ (also genitive because it describes شركةٍ).
  In normal unvowelled writing, these endings are usually not shown.

Common negation options:

• لا أعمل في شركة كبيرة في هذه المدينة. = I do not work in a big company in this city. (general/habitual)
• لستُ أعمل... can occur, but لا + imperfect is the most straightforward for learners in MSA.