When latest Autumn spreads her evening veil (1)
Hm. The season Autumn is getting personified as a lady wearing an "evening veil." People wear veils to hide themselves, or part of themselves. This is an odd way of describing the way darkness spreads at dusk during the fall months. It seems like no coincidence that a female poet, who was very self-conscious about how she was exposing herself to criticism for writing poetry at all, would include this image of a woman wearing a veil.
Oft seems to fleet before the poet's eyes; (6)
Charlotte Smith doesn't say "my eyes." Instead, she refers to herself in a kind of distanced and universal way as "the poet." It seems like she wants to emphasize the fact that she's a poet, and therefore has stuff in common with all other poets, male and female.
Here, by his native stream, at such an hour,Pity's own Otway I methinks could meet, (9-10)
The speaker imagines that she might meet the ghost of the poet and playwright Thomas Otway (check out the "Best of the Web" for more info on him). He was a poet that Smith particularly admired, but it's important that he's a male poet. Smith seems to want her readers to think of her as part of a broader English poetic tradition, and not just as a lady poet.