Is it permissible to give charity with the intention of removing a specific affliction, such as resolving marital disputes, or with the intention of increasing blessing in wealth and offspring, while considering it done for the sake of Allah's pleasure? And is it permissible to utter the intention aloud, or should it only be in the heart?

There is no harm in giving charity with the intention of warding off evil or attracting good. This is a permissible form of seeking intercession through good deeds and does not contradict sincerity. It is preferable that the intention be purely to seek closeness to Allah, and you will receive the worldly recompense promised for charity. There is no need to vocalize the intention, as its place is in the heart.