> Когда светило дня к полуночи взирало,
> When the sun of day looked toward north

"Светило" is abstract "source of light", but in most cases this word means "sun".
It's very unusual today to see "полуночь" in meaning "north (lands)".

Стенящу, страждущу Россию обретало.
It found moaning, suffering Russia.

В ее объятиях рожденная Казань
In her (Russia's) embraces Kazan (being) born

Из томных рук ее брала позорну дань;
Out of her (Russia's) weak/languishing hands took a shameful tribute

Сей град, российскими врагами соруженный,
This city built by Russian enemies

На полночь гордою горою возвышенный,
In the north elevated on/by a proud mountain

Подняв главу свою, при двух реках стоит,
Lifting its head, stands at two rivers,

Отколе на брега шумящей Волги зрит.
From where it views the banks of the resounding Volga

Под тению лесов, меж пестрыми цветами
Under the shade of forests, amidst multicolored flowers

Поставлен Батыем ко северу вратами,
Located/placed by Batu with gates toward the north,

Чрез кои в сердце он России выбегал,
Through which he (Batu) rushed out into the heart of Russia

Селенья пустошил и грады пожигал.
Devestated villages and burnt cities

С вершины видя гор убийства и пожары,
From the peak of the mountain viewing the murders and fires,

Где жили древние российские болгары,
Where lived the ancient russian Bulgars

Разженны верою к закону своему,
Filled with belief in their law,

Казань, поверженна в магометанску тьму,
Kazan, plunged into Muhammadan/Islamic darkness

В слезах на синий дым, на заревы взирала
In tears (Kazan) gazed at the blue smoke, (and) blazes

И руки чрез поля в Россию простирала;
And stretched across the fields its hands into Russia

Просила помощи и света от князей,
Requested help and light from the princes

Когда злочестие простерло мраки в ней.
When evil stretched its shadows in it

Подвигнуты к странам природным сожаленьем,
Moved by natural pity for the countries

Народа своего бедами и томленьем,
by the troubles and misery of their own people

На части полночь всю расторгшие князья
Having divided/broken up all the north the princes

Смиряли наглых орд, во бранях кровь лия.
Suppressed the arrogant horde(s), shedding blood in battles.


It's amazing that you can do this translation, because it's hard text for modern native russian speaker too.
I think many words have shifted their meanings in some way throught hundrends of years which passed since writing this poem and many phrases looks strange/twisted now. Probably modern native russian speaker cannot understand it's mental image in all depths.
However overall meaning is clear: Kazan was founded in Volga Bulgaria State and later was conquered by Golden Horde which made it large important centre between Russia and Horde - important city at the cross of routes. Later it was conquered by Russia.
Today Kazan is capital of Tatarstan Region of Russia - nearly half of population are tatars - descedants of population of Khanate of Kazan.