This night in Iran is the longest night ( shabe yalda) :)

Dimming Sky, Brightening Lights.

Twinkling stars, Empty streets.

Drinking alone, with tears of lovesickness.

Rejoicing with the Moon,  through the waning winter.

The dimming sky, brightening lights.

The twinkling stars but empty streets.

Excellent semantic translation.  However, in the last light, I see no translation of "invitation".  Translation should contain as much as possible of the keywords of the original and if omitted, the meaning must imply that idea.  Your first three lines fulfilled such a requirement.

Exactly, I tried serveral times to fit "invitation' in the last line, but failed. Uhm... I think maybe I need to make a minor change to make it look better. 

Rejoicing With the invited Moon, through the waning winter. So 邀（inviting) and 同庆 （rejoycing together) are gonna be translated with nothing ommited.

You can also translate the last line as,

The invited moon, my boon companion through the waning winter.