What are the epic conventions in Book 1 of Paradise Lost?

Milton engages the reader immediately with his purpose, just as Homer and Virgil do, as well as the "modern" Italian poets Ariosto and Tasso. In epic convention there is an announcement at the start that the poet "sings" his subject, though Milton makes the verb imperative in writing:

Sing, Heavenly Muse

The opening page of an epic is generally devoted to a kind of summary of the action and purpose of the work. Here Milton, though reproducing the manner of the classical poets, tells us what differentiates him from them. This is not to be a work about earthly battles and purely human conflict. There is a religious purpose too:

. . . justify the ways of God to men.

Milton also asserts that his poem will accomplish:

Things unattempted yet in prose or rhyme.

Probably all of the epic poets have intended to do just that, though perhaps without proclaiming it so boldly. But after this brief introduction, Milton continues to follow the convention of a direct plunge into the action, which here is nothing less than the fall of Satan and his comrades into the infernal regions.

Typical to epic poetry is the central subject of a huge battle or war, of course. In the Iliad, it's the Trojan War; in the Aeneid, it is also the Trojan War (at its final moment as a prelude to Aeneas's adventures that will lead to the birth of the Roman people). In Paradise Lost, it is the war between Satan against God (and eventually, against man).

Some would say the most decisive characteristic of an epic poem is the presentation of a hero: in the Iliad, it is Achilles; in the Odyssey, it is Odysseus; and so on. But in Milton's work, who is the hero? The Romantic poets, who idolized Milton—but were themselves secular and irreligious—believed it was Satan. In a technical sense, Satan does appear to be the hero in the first two books of Paradise Lost. He is the center of the action; he rallies his "men" around him, and he even has the qualities of determination and strength we associate with the heroic. It's an enormous irony, of course, that Milton created such a character while putting forth what he intended as an ultimate message of religion and faith.

What epic characteristics are found in Book 9 of Paradise Lost?

Strictly speaking, an epic is a long narrative poem on a great and serious subject. It is written in an elevated style, and has at its centre a heroic or quasi-divine figure on whose actions the fate of many people depends. The setting is huge, often worldwide, or even larger.

 Paradise Lost clearly fits the criteria, taking as its subject the Fall of Man, and having the elevated purpose of setting out to 'justify the ways of God to men'. The hero could be seen to be Adam, whose fatal action 'brought death into the world/And all our woe', or Christ, who redeemed that fault, and was both God and man.

 Book 9 is in some ways less obviously epic in method and scale than the other books. Milton opens it by declaring a change of mood ('I now must change/These notes to tragic') and the whole book has quite a dramatic quality, with soliloquy and impassioned debate, temptation and recrimination between its protagonists. Milton invokes his heavely Muse, however, to inspire his work and, although the scenes in the garden are more domestic in scale than the earlier books, we still get the cosmic perspective as Satan circles the world, seeking his entrance to achieve his evil purposes. As elsewhere, Milton uses a number of extended epic similes, including a memorable one when Satan observes Eve in her pastoral setting and is, temporarily, almost abstracted from his own evil.  

What characteristics make Paradise Lost an epic?

The standard definition of an epic, or heroic poem, is that it is a ''noble story told in noble verse'' (Hutson and McCoy, Epics of the Western World, p. 7), a continuous narrative concerning a heroic person from history or tradition.

The epic is an extended narrative dealing with a hero or group of heroes attempting to achieve a specific goal. This goal frequently has to do with actions, events, or ideas that tend to define a culture either through history, values, or destiny, or, at times, all three. Any poem can be heroic, but the epic is separated from other heroic narratives through its magnitude and style. In simplest terms, epics are very long and written in a highly elevated style. 

The fate of humankind thus becomes the unifying force of the poem, as Milton presents the ideals of private virtue and public rectitude by exploring both the nobility and weakness of fallen humanity.

Like the classical epic, Paradise Lost alternates its setting between the world of men and the worlds of God and the angels (fallen and unfallen). As well as the typical epic forms described above, a number of epic motifs are incorporated by Milton into the poem. For example, he incorporates mythology, though it is Biblical, not classical, myth which dominates Paradise Lost.

Although he claims that war, the traditional subject matter of the epic, is not to be his theme, he does incorporate the motif of battle into the poem.