Work for a TOC but non-safeguarded. Thanks for the clarification - I thought that might be the case.
In that case, your entitlement for the first and second journey scenarios is as follows:
- From Tottenham Court Road to Slough (Core section to NR)
As mentioned by others, the best way of getting discounts within the 'core' section of the Elizabeth line is to use an Oyster card with the Priv "National Rail" discount set.
Unfortunately, as Slough is outside the Oyster area of validity, you have to touch in/out somewhere within the Oyster area when you switch between Oyster and the paper/smartcard ticket you're using for the remainder of your journey. That's likely to involve a degree of inconvenience.
Arguably, this would be best done at Paddington, as most trains have a slightly longer stop there. If you make sure you're in the ideal coach (3 or 7), you may just manage to make it back onto the same train after quickly walking up the short escalator, exiting the gateline with your Slough <-> London ticket, then touching back in with your Oyster card (or vice versa).
If you don't make it onto the same train, in the eastbound direction it wouldn't be long until the next one - which would start at Paddington, thus guaranteeing you a seat. In the westbound direction, I would suggest aiming for a Paddington terminator at Tottenham Court Road and then changing onto a Maidenhead/Reading train at Paddington.
Unfortunately if heading westbound in the evening peak, there is virtually no chance you're getting a seat at Paddington - and you may not even be able to physically get onto the train, such is the level of crowding a lot of the time.
- From Paddington to Liverpool Street (fully within core section)
You can either use Oyster with the Priv "National Rail" discount set (this is cheapest and valid for either leisure or commuting purposes), or buy a special Priv-rate paper fare valid only on the Elizabeth line core section (Paddington-Abbey Wood). The latter costs £1.75 single/£3.50 return and is only valid for leisure travel.
How about for someone who is not safeguarded and doesn't work for a TOC or NR? Someone who has reciprocal priv travel facilities.
It depends very much on the precise details of the reciprocal travel facilities, i.e. which employer gave them.