Will God's compensation to whoever gives something up for His sake be of the same kind, and will it be in this world or the Hereafter? And is it possible that God might not compensate him with something better than what he gave up?

It is mentioned in the authentic Hadith: "Indeed, you will not give up anything for Allah, the Almighty, but Allah will replace it with something better for you than it." This replacement may be of the same kind as the thing abandoned or of a different kind, and it may be in this world or the Hereafter. In this world, the compensation is sometimes an increase in intimacy with Allah and love for Him, or tranquility of heart, or lawful provision. As for the Hereafter, the compensation is greater, as the entire world does not equal a speck of what is in Paradise, such as the garments of faith or the houris. The compensation is assured as long as the abandonment is purely for the sake of Allah, and it is from Allah's provision contingent upon His will. What is with Allah cannot be attained by disobeying Him.