Is it permissible to supplicate for miracles from Allah (Exalted is He), knowing that uprightness is better, and with the intention of increasing faith and spreading the Da'wah? Is this considered an excess in supplication, and what is the ruling on one who seeks out times of response for this purpose?

There is no harm in asking Allah to honor a servant with an extraordinary karamah (miraculous boon); because there is no prohibition against it, and a karamah is not impossible to occur, rather it is frequent. Examples include the prayer of the three men in the cave asking Allah to remove the boulder from them, and the man who cast his money into the piece of wood in the sea, and the supplication of Al-Alaa bin Al-Hadrami, who marched with his army across the river. The intention of the supplicant must be pure for Allah Almighty, and he should intend by it closeness to Allah, and there must be a need that calls for such a request. As for asking Allah for ordinary impossibilities, such as requesting a child without intercourse, it is forbidden and a sign of disrespect.