I would need to seek approval to book outside of policy. I probably could do it anyway without approval, but if I did it would likely be queried when the invoice for the booking arrived (typically around 10 days after travel). It's all charged centrally and then the cost is allocated to wherever it needs to go.
POUGS would be charged in the same way as above.
What does your T&S policy say about upgrades or out of policy class of travel? Ours just says they are at our own expense so I'd note the difference between the fares as evidence (take screenshots ) and claim only the lower amount. The rest of it is either offset against my expenses or indeed future expenses, or else I pay the amount manually.