Learn Polish: Sukces firmy opiera się na wiarygodności i dobrej komunikacji. - The company's success is based on credibility and good communication.

They are governed by the phrase opierać się na (to be based on). When the preposition na is used with this verb to describe the foundation of something, it always requires the following nouns to be in the Locative case.

Could we swap opiera się na with polega na in this exact sentence?

Grammatically yes, as both require the Locative case, but the meaning shifts. Opiera się na means 'is based on' (acting as a foundation), while polega na means 'consists of' or 'lies in'. Using polega na would imply that the success essentially IS the communication itself, rather than being built upon it.

The dictionary form of credibility is wiarygodność. Why does it end in -i here?

Feminine abstract nouns ending in the suffix -ość are very common in Polish. Their Locative form is made simply by adding -i to the end of the word, turning wiarygodność into wiarygodności.

Why does the feminine noun komunikacja become komunikacji in the Locative, instead of taking the typical -e ending?

Nouns ending in -cja (which are usually loanwords like komunikacja or informacja) are an exception to the standard feminine declension. Instead of taking an -e in the Locative case, they always take an -i.