In reply to jasonpather:
> 2. Is it acceptable to climb indoors in approach shoes and just do steep endurance boulder stuff that doesn't put much weight on your feet?
I'd say ask at the desk first -- explain you've got a foot pain problem and can't use climbing shoes at the moment and ask if it's okay to climb in approach shoes. Obviously it's up to whoever's on duty, but I've done this on occasion in the past and the staff have been understanding and fine with it.
Some places (including the Arch) have a "no outdoor shoes on the mats" type rule, so it's better to explain and ask permission so they don't think you're just wandering round in grubby trainers.
> I think I need a really supportive stiff climbing shoe and don't want to stop climbing and training.
How long's the pain been going on? If your regular shoes work well for you, you might not want to invest in a pair of super-stiff shoes unless it's clear (after seeing a doctor) that the pain is going to be a long-running thing.
All that given: obviously, the best shoes depends on what suits your foot shape and climbing needs, but hopefully people can give you some leads to try. Alas, the Five Ten Galileo (which saw me through my foot injury) is no longer available. But you can still find the Boreal Ballet (which is board-lasted), and I believe the Evolv Astroman is very stiff. I've also seen the Five Ten Verdon mentioned as a stiff shoe, and that may be more technical. The Five Ten Hiangle is stiff and also downturned, if that turns out to be easiest on your feet.