Glad you have an appointment booked
The lumpiness in the belly sounds similar to what our robo had (without seeing it). He had a few lumps - but one that got quite large. It didn't seem to bother him for a long time - he was on metacam the last few months though. It is possible he has tumours. But the eye may be something else. Hope the vet can help. I would say to her when you go in, that he is very nervy. I don't think a vet should scruff a hamster tbh - I believe that is out of fashion and considered not good for them. If your hamster bites her because she's not gentle enough - tough! At least it'll be over with fairly quickly. They can take a few days to settle afterwards but I'm sure he'll get over it.
This was the box I used. Not too big to take with you but big enough for a hamster to have a little hide and a wheel and a tunnel in.
https://www.amazon.co.uk/gp/product/...?ie=UTF8&psc=1