Planning the following Itinerary on Oneworld: CX HKG-LHR (F) (22/6) BA LHR-MAD (Club Europe) (22/6) IB MAD-GVA (J) (27/6) BA ZRH-LHR (Club Europe) (3/7) CX LHR-HKG (F) (6/7)

Planning the following Itinerary on Oneworld:

CX HKG-LHR (F) (22/6)

BA LHR-MAD (Club Europe) (22/6)

IB MAD-GVA (J) (27/6)

BA ZRH-LHR (Club Europe) (3/7)

CX LHR-HKG (F) (6/7)

By this itinerary, am I eligible for accessing the following lounges?

1. CX The Wing F + CX The Pier F

2. Qantas Hong Kong Lounge

3. BA Galleries First T5 + First Dining Room

4. BA Galleries First T3 + First Dining Room

Yes

Unless you're OWE, you don't be able to access the First Class lounges at LHR T5, for the EU regional flights. You will of course get access to the LHR T3 lounges since your onward flight with CX is in first. 

is that flight connection with a long-haul first will gain First lounge access?

https://www.oneworld.com/ffp/lounge-access

Yes you are right.

So you can access the T5 First class lounge assuming 22/6 means 22 June i.e. you're connecting from the CX first class flight.