Learn Farsi: شاید من فردا در سمینار حضور داشته باشم. - I might be present at the seminar tomorrow.

The word shâyad (maybe/might) expresses doubt or possibility. Just like the impersonal expression gharâr ast (it is planned) that you are focusing on in this lesson, shâyad requires the action that follows it to be in the subjunctive mood.

I don't see the usual be- prefix for the subjunctive. How is hozur dâshte bâsham formed?

The infinitive here is hozur dâshtan (to be present, literally 'to have presence'). The verb dâshtan (to have) has an irregular subjunctive pattern. Instead of adding a be- prefix, you use its past participle dâshte followed by the subjunctive forms of 'to be' (bâsham, bâshi, etc.).

Does shâyad always have to come at the very beginning of the sentence before the subject?

Not always. While shâyad often sits at the very start of the sentence, it is also very common to place it directly after the subject. Saying man shâyad fardâ... would be just as correct and natural.

The sentence talks about tomorrow (fardâ), so why is the verb in the present subjunctive rather than a future tense?

Farsi does not have a specific future subjunctive form. Whenever you express a possibility or expectation about the future using triggers like shâyad or gharâr ast, you just use the present subjunctive. The time marker fardâ gives all the future context you need.