Multiple Criteria Look up: Which Function to use?

[AmateurHour]

I am trying for a formula to cross reference between the number of sessions John Doe has purchased and the days they are valid to then countdown each time a session is used up.
Formulas to go in the following columns:
Column F for the Gym locations
Column G for the Outdoor locations

Screenshot 1 is the Block booking tab (where it tells me who has paid for what and how many sessions- Column E).
Screenshot 2 & 3 are where the register is taken as to who came to which session date. 2 being January, 3 being July.

I would like the Block booking tab to search the other tabs for the name of the individual and show me how any sessions have been used within the qualifying dates and show me when they have used all their sessions from the block. Which may be before the expiry of blocks.

For example John Doe has purchased 2 different blocks.
In Screenshot 2 he used up his last session from "GYM 4" block on 6th Jan.
In Screenshot 3 he has used up 3 of the original 8 and so only 5 left.

Any help would be much appreciated.

 

[AmateurHour]

Just nudging this.

 

[hagia_sofia]

As it seems that each month is represented by a separate sheet and with the assumption that the numbers of people vary between individual months it would probably be much easier if your data is structured differently, i.e. one big table with 4 columns, i.e. date, track, name, and values (or maybe 6 columns, i.e. even with coach and programme) - cf. the picture. This would allow to look for the necessary data within one sheet.