If a final exit door in a public area has a push bad engraved 'push', does it still need a 'push pad to open' sign? I initially would've thought not, but thinking about hours of darkness or during emergency lighting cover, this probably wouldn't be visible/clear.

Do we also need 'fire exit, keep clear' signs on the back of these doors if it's all clear glass?

I would advise Fire Exit Keep Clear signs on both sides. The existing PUSH sign should be sufficient unless the Fire Risk Assessment requires illuminated signs. 

Strictly speaking if it's text only it doesn't meet the requirements for fire safety signs under the Health & Safety (Safety Signs & Signals) Regulations 1996 as it does not include a pictogram (symbol/picture) - however I take a balanced approach to this based on the potential number & type of users of the exit as the most common symbol you see is just a white tick on green which adds nothing to understanding how to use the door.

If the exit has the required level of emergency lighting adjacent it won't need to be photoluminescent as it would have suitable external lighting (plus  photoluminescent signage isn't very effective unless externally lit continuously to keep the material 'charged' so it has the required brightness and duration of luminescence to be any use when the power fails) 

Thanks. Good to know about the Health & Safety (Safety Signs & Signals) Regulations 1996