Ben modüllerin yerleştirilme sürecini izlerken, ekip üyeleri tasarım hatalarını düzeltiyordu.

• In Turkish, when a verb stem ends in a vowel (here izle-), you insert a buffer consonant r before a vowel-initial suffix.
• The suffix -ken attached to a verb stem means “while doing X.”
• So izle + r + ken → izlerken = “while (I) watch/watch(ed).”

• Here izlerken is an adverbial clause (“while watching”), not a full finite verb form.
• The main clause carries the past-continuous meaning with düzeltiyordu.
• If you wanted the subordinate clause itself to show past continuity you could say izliyorken, but it’s not required: -ken alone is enough to indicate simultaneity.

• The entire noun phrase modüllerin yerleştirilme süreci functions as the direct object of izlemek (“to watch”).
• In Turkish, a definite/specific direct object takes the accusative suffix -i (harmonized here to -ini), so süreci → sürecini (“the process”).

• yerleştirmek = “to place.”
• Adding the passive suffix -il gives yerleştirilmek = “to be placed.”
• Then nominalizing with -me produces yerleştirilme = “the placement” or “the act/process of being placed.”

• Base verb: düzeltmek = “to correct/fix.”
• Present-continuous: düzeltiyor = “is fixing.”
• Add simple-past -du → düzeltiyordu = “was fixing.”
• The -yordu form (present-continuous + past) signals an action that was ongoing at a certain past moment.
• In contrast, simple past düzeltti would mean “fixed” (a completed action).

• ekip üyeleri (“team members”) is the subject of the main clause.
• Subjects in Turkish are typically in the bare (nominative) form without a suffix.
• The verb ending -yor + -du already tells you it’s third person plural, so no extra marking is needed.

• tasarım hataları (“design errors”) is the direct object of düzeltmek.
• Because these errors are definite/specific in context, Turkish uses the accusative -ı (harmonized to hatalarını).
• If you wanted a non-specific meaning (“some design errors”), you could drop the accusative: tasarım hataları düzeltiyorlardı.

• Turkish verbs often encode person/number, so pronouns are optional.
• ben (“I”) is added here for emphasis or clarity: “As for me, …”
• You can remove ben without changing the core meaning:
“Modüllerin yerleştirilme sürecini izlerken, ekip üyeleri tasarım hatalarını düzeltiyordu.”

Yes. Instead of nominalizing with -me, you can use a relative clause:
• modüllerin yerleştirildiği süreç = “the process in which the modules are placed.”
• As a direct object it becomes: modüllerin yerleştirildiği süreci izlerken, …
Both versions are correct; -me focuses on the noun “placement,” while -diği explicitly turns it into a “that-which” clause.