Ruling on one who prays but does not pay zakaah or fast, or one who does Hajj but does not pray
Question

I read in some of your answers that if a person fasts but does not pray then his fasting is not valid. What about the opposite; if a person prays but does not fast, or prays but does not pay Zakat, or performs hajj but does not pray?.
Praise be to Allah.The one who does not fast Ramadaan because he denies that it is obligatory is a kaafir and his prayer is not valid. The one who does not do it deliberately and out of carelessness is not a kaafir, according to the correct view, and his prayer is valid. The one who does not pay the obligatory zakaah because he denies that it is obligatory is a kaafir and his prayer is not valid. The one who does not do it deliberately and out of carelessness is not a kaafir and his prayer is valid. The same applies to Hajj; the one who does not do it because he denies that it is obligatory is a kaafir, but the one who does not do it although he is able to do it is not a kaafir and his prayer is valid. 
Fataawa al-Lajnah al-Daa’imah li’l-Buhooth al-‘Ilmiyyah wa’l-Ifta (10/143, 144) 
The one who does not pray is a kaafir and an apostate according to the correct scholarly view, so no act of worship that he does is valid. 
See the answer to question no. 5208.