Praise be to Allah.
It is not saheeh; it is a da‘eef (weak) hadith that is not soundly narrated. Rather what is proven mentions the prayer only; one prayer in al-Masjid al-Haraam is equivalent to one hundred thousand prayers offered elsewhere, and one prayer in the Mosque of the Prophet (blessings and peace of Allah be upon him) is better than a thousand prayers offered elsewhere. As for fasting, there is no proven report about it, except for a da‘eef hadith which says that it [fasting Ramadan in Makkah] is better than one hundred thousand elsewhere. But it is da‘eef (weak). However, righteous deeds have a special virtue when done in Makkah; fasting, giving charity, reciting adhkaar and other righteous deeds have a special virtue. But there is no evidence to prove the degree to which they are better (than righteous deeds done elsewhere), apart from prayer. End quote.