Learn Turkish: Durum çok zor, sana açıklayayım mı? - The situation is very difficult, shall I explain it to you?

The verb root is açıkla (to explain). To add the 'shall I' ending taught in this lesson, we use the optative suffix -a. Because the root ends in a vowel, we need a buffer y before adding that suffix, and another before the 'I' ending -ım. So it breaks down as: açıkla + y + a + yım.

Could I use the future tense açıklayacak mıyım instead of açıklayayım mı?

They mean different things! Açıklayacak mıyım? is a factual question about the future: 'Am I going to explain?'. Açıklayayım mı? uses the optative mood, which makes it an offer or a suggestion: 'Shall I explain?' or 'Do you want me to explain?'.

Why use sana instead of seni here?

The verb açıklamak (to explain) directs the action toward someone. In Turkish, you explain something to someone, which requires the dative case. Sen (you) changes to sana (to you). Seni is the direct object form, which you would use if you were explaining the person themselves!

Where is the word for 'it' in the Turkish sentence?

There isn't one! In Turkish, if the object of the verb is already obvious from the context (in this case, the difficult situation), pronouns like 'it' are often left out entirely.