fairykisses stillno is absolutely right, total intravenous anaesthesia (TIVA) is associated with less PONV, but there are so many variables. Agree that the best thing to do is mention it to your anaesthetist and get a load of anti emetics on board before you wake up.
georgedawes lots of patients need a bit of oxygen for a few hours post -op. Its usually nothing to be concerned about, but yes, do mention this to your anaesthetist next time. Even the smallest details can be important.
Wednesbury without looking at your notes it's hard to know exactly, but I concur with stillno that the most likely candidate is Syntocinon (a synthetic version of the naturally occurring hormone oxytocin) or possible Syntometrine which is a combination of Syntocinon and ergometrine. It is used to make the uterus contract after birth and control bleeding post delivery. Every patient who has CS will receive it.
With regards to your second question, it's quite difficult to answer. There are many ways to give an anaesthetic and everyone practices slightly differently. For a major surgery we won't give 'more' anaesthetic exactly, but because its likely to last longer your total exposure to anaesthetic drugs will be more. (I don't know if that makes any sense to you?) with major surgery we are also likely to give you a load of opiates for pain releif which can leave you feeling totally 'out of it'.
I'm sorry you didn't have a good birth experience, but please don't beat yourself up over it. There as nothing you could have done and I'm sure you are the most wonderful mother. Even years later counselling can help if you are interested. There are some therapists that specialise in medical counselling and even just one session might prove beneficial. I do think its a service that should be more widely publicised.
chestynut before your surgery make sure your asthma is really well controlled. Avoid (even more than usual) smoke, pollen, dust anything else that irritates your lungs.
Try to make sure you are as fit as you can be. If you use an inhaler, bring it to the anaesthetic room with you and take a few puffs before induction.
If no other medical conditions are present, propofol is the induction agent of choice in asthmatics. I know what you mean about it hurting though. Some people find it just a bit cold going up the arm, others find it unbearable! Mention it to your anaesthetist because there are things that can be done to make it hurt less. Finding a big juicy vein helps! Being warm and well hydrated helps to get those veins up. (Although when you are told to stop eating and drinking pre-op, it's really important that you do stop. I'm sure you know that anyway)
After consultation with your anaesthetist he may decide to use something else, but if he doesn't, remember going to sleep with propofol takes 30 seconds at the most. 
An ODO is an operating department orderly. Think they are all called porters now, ODO is the old name for them and I'm showing my age! 
It's a rare day that I get a break at work and if I do it's never long enough to get changed and leave theatres. So I give the porters money to buy me coffee and sandwiches from the shop. Honestly, it is the 'little guys' like the porters, cleaners and health care assistants that keep us off our knees!
Right will be back to answer more of the questions after tea.
You've asked some interesting ones 