The Network Railcard cannot be used (much) before 10:00; there are a few journeys when it can be started before 10:00, where it would otherwise be unreasonable to restrict the use of the railcard to 10:00 (e.g. 09:20 from Weymouth to London) and the final arrival time into London is going to be a long time after the morning rush has ended.
Any easement on the Network Railcard applies to stations some distance from London, and won't help with an early journey from Twickenham to Tonbridge.
What, however, you can do is start your journey on Contactless before 0630, travel to Sevenoaks, then use a full price 'paper' ticket (or e-ticket) fron there to Tonbridge. You would need to leave the train at Sevenoaks, and catch the next one having touched out on the barriers.
Yes, this would work to "step back" a train at Sevenoaks.
Alternatively, it's £37.30 for a day return valid via London Waterloo, which is the most straightforward option.
If you want to travel via London Waterloo as quickly as possible on the outward portion, but don't mind the slower option via Redhill on the return, it may be cheaper not to buy a return and instead to buy singles each way, using the Railcard on the return portion. (It may be even cheaper to further split this down by using Contactless for part of the journey), but the saving would not be much, so it's probably not worth it.
On the return journey you may be able to discount a through ticket using the Network Railcard.
Yes, it would be £13.05, if avoiding Waterloo and changing at Redhill, or £16.70 via London Waterloo, for a single from Tonbridge to Twickenham, with the Railcard discount.
