Learn Farsi: ورزشکاران برای افزایش استقامت جسمانی شروع به دویدن می‌کنند. - The athletes start to run to increase physical stamina.

shoru' kardan (to start) is a compound verb. When used with the preposition be (to) and an action, the preposition and the action often go between the two parts of the compound verb. So we get shoru' + be davidan + mikonand (literally: they do a start to running).

Why do we use the full infinitive davidan here? Don't we usually use the subjunctive for the second verb in a sentence?

You are right that verbs like 'want' or 'can' trigger the subjunctive. However, the phrase shoru' be is an exception. The preposition be requires a noun, so we use the full infinitive davidan (running/to run), which acts as a verbal noun here.

How does the grammar of the phrase afzāyesh-e esteqāmat-e jesmāni work?

In the English translation, 'increase' acts as a verb ('to increase'), but in Farsi, afzāyesh is a noun meaning 'the increase'. The ezafe connects the noun afzāyesh to esteqāmat (stamina) to mean 'the increase of stamina', and then links that to the adjective jesmāni (physical).

Why is the plural suffix -ān used for varzeshkārān instead of the usual -hā?

While varzeshkār-hā is perfectly correct and more common in everyday speech, is a plural suffix used specifically for people and living things. It gives the sentence a slightly more formal or written tone, which matches the advanced vocabulary used here.