This is not meant to be definitive nor exhaustive, but merely an exploration of certain themes and symbols in the poem:
Yeats is widely regarded as one of the great poets of the ages--Eliot considered him the greatest poet of the 20th century--and is certainly of similar stature with the greatest poets of antiquity. Thus his innovations regarding subjects such as mythology can be taken as new additions to canon. Linking his use of Aengus to previous stories is not essential, where choosing the mythological figure associated with poetry conveys meaning merely for the choice.
"Love, youth and poetic inspiration" are clearly the central themes of this poem. (Insight might be found in Yeats not having choosen Oisín as the protagonist, as that choice could be said to carry different significance.)
However, there is a direct reference to the The Dream of Aengus in that Aengus was said to have fallen in love with a girl he'd seen in a dream, and pursued her until he found her. Yeats is certainly transfiguring this story from mythology into a new form that carries new meaning. [As a referent, you may want to read Yeats' plays dealing with the Ulster Cycle.]
"And caught a little silver trout"
This instantly brought to mind the Salmon of Knowledge, which is due no doubt, in part, to the opening of the stanza "Because a fire was in my head", where head can be taken as "mind". Perhaps Yeats was being playful in recasting this legendary fish as a "little silver trout". (In other words, the poet is not to receive all the knowledge of the world, merely a little piece. Clearly the poet places less value on knowledge than love, which is consistent with Yeats, who could be quite romantic: "Wine comes in at the mouth" and so forth.)
Note that the Salmon of Knowledge was elevated from common fish status by eating 9 hazelnuts. Unlike Fionn, Yeats doesn't have a chance to cook the fish and gain its benefit, being distracted by a girl.
The author's use of a "hazel wood" is not random--hazel wood was said to be sacred to poets, and thus proscribed for use in the hearth, which is doubly interesting in that it is presented in a fire context. Possibly Yeats' meaning is that the fire of inspiration cannot be restrained, for is use of fire is clearly meant to mean inspiration. [More on hazel in the Celtic tradition can be found here.
The apple tree also has meaning in Celtic lore. The proposed meanings both work in the context of the poem: "fruitfulness" as in fertility and sexual maturity/appeal; "immortality" in that the girl is ethereal and likely represents an ideal.
The poet is do distracted by the girl, he forgets what he was doing and spends the rest of his life pursuing her, who, as an ideal, is ultimately unobtainable. But for the poet, this is useful, as it leads to a lifetime of inspiration (striving to reach the ideal) and results in this, and many other, poems.
"golden apples of the sun"
This has several references, all of which Yeats would have been intimately familiar with, deriving from Classical Mythology, which he draws on extensively in other poems, and Norse Mythology (Ireland was subject to Norse migration), as well as Irish mythology.
The Irish reference is to the "Silver Branch" and linked to mortality, apropos as the poet is now old, and a poet should "not go gentle into that good night", as a later prince of the form would comment.
The Greek reference is to the Garden of the Hesperides and linked with immortality, an interesting juxtaposition.
The Norse reference is to Idunn and linked to fertility, here clearly in the context of the mind (i.e. creativity.)
On silver apples I have no direct reference. Possibly the poet was being poetic and playful, and the meaning of the silver apples can be inferred by their contrast to the golden apples. The Sun and Moon are linked in both Greek and Norse mythology, with the transposition of male/female nature in the respective traditions. (In Norse Mythology, the sun is female and moon is male, the opposite of Greek Mythology.) Possibly we can take the silver apples to mean mortality, in contrast to the golden apples.
Also worth noting that orange blossoms are associated with marriage and used by Lorca in Blood Wedding. Both poets were certainly referencing, in part, the idea of the "Great Marriage" or "Sacred Marriage" to the "Great Goddess", which should be understood in the context of Adonis as representing death.
You may find the poet's "Two Songs from a Play" useful, as it draws heavily on Classical literature, and touches on some similar themes:
Everything that man esteems
Endures a moment or a day.
Love's pleasure drives his love away,
The painter's brush consumes his dreams;
The herald's cry, the soldier's tread
Exhaust his glory and his might:
Whatever flames upon the night
Man's own resinous heart has fed.
In a practical sense, it is the state of un-fulfillment that drives the artist, they journey so to speak, as opposed to the achieving of the goal, which is death, at least creatively speaking.