Saints at last to probe lacking heart for nil-nil? (2,5)

'saints at last to probe' is the definition.
I know nothing about this answer so I cannot tell whether it can be defined by this definition.

'lacking heart for nil-nil?' is the wordplay.
'lacking' becomes 'no' (eg lacking money means with no money).
'heart' becomes 'core' (synonyms).
'for' means one lot of letters go next to another (I've seen this in other clues).
'nil nil?' becomes 's' (I can't explain this - if you can you should give a lot more credence to this answer).
'core' put after 's' is 'score'.
'no'+'score'='NO SCORE'

Can you help me to learn more?