Learn Farsi: اگرچه شاعر جوان است، شعر او خیلی محبوب است. - Although the poet is young, his poetry is very popular.

Because agarche (although) states a real, established fact: the poet is actually young. Even though it contains the word agar (if), which often takes the subjunctive for hypothetical ideas, agarche pairs with indicative (regular) tenses like the simple present.

Could I use bâ inke instead of agarche here?

Yes, they both mean 'although' or 'even though' and use the exact same grammar. agarche sounds a little more formal and is often used in writing, while bâ inke is very popular in everyday spoken Farsi.

Are the words for poet (shâ'er) and poetry (she'r) related?

Yes, they share the same Arabic root letters. shâ'er is the active person who writes, and she'r is the poem or poetry itself.

How does the phrase she'r u translate to 'his poetry'?

The two words are linked by the invisible ezâfe vowel, pronounced 'e'. When spoken, it connects them as she'r-e u (literally: poetry of him). Remember that Farsi pronouns don't have gender, so u could just as easily mean 'her' depending on who the poet is!