Learn Farsi: ما باید کتباً اعتراض کنیم تا کیفیت خدمات بهتر شود. - We must complain in writing so that the service quality gets better.

No, because they serve entirely different functions. be dalil-e inke gives a reason for something that is a fact, and it takes the indicative mood. tâ here means "so that," introducing a future goal or purpose. Goals require the subjunctive mood, which is why we see the subjunctive shavad at the end of the sentence instead of the indicative mishavad.

What is the special symbol at the end of the word katban (کتباً)?

That symbol is called "tanvin" and it makes an "-an" sound. It is borrowed from Arabic and is used in formal Farsi to turn a noun or adjective into an adverb. Here, it turns a root meaning "written" into the adverb katban (in writing). You have likely seen this before in the common word vâqe'an (really).

Why doesn't the compound verb e'terâz konim have the continuous mi- prefix?

It is in the subjunctive mood because it follows the modal verb bâyad (must). The infinitive is e'terâz kardan (to complain or protest). To form the subjunctive for "we", the mi- prefix is dropped from the present stem, leaving just konim.

Since khadamât (services) is plural, why does the verb shavad stay singular?

The true subject of the second clause is keyfiyat (quality), which is singular. In the connected phrase keyfiyat-e khadamât (the quality of services), the verb always agrees with the first, main noun. Additionally, even if the subject were "services," inanimate plural nouns in Farsi generally take singular verbs anyway!