I'd agree with most of that - extradition's usually limited to crimes more serious than a certain level (carrying X years in prison, for example) and as a practical matter, a government won't bother pursuing extradition for parking violations even if it could in theory. Whether it's a crime in both countries can be a useful safeguard though: countries like Saudi Arabia have strict religious laws against promoting or even practicing religions besides Islam, Thailand has laws against insulting their King, but I'd be shocked to see the US or UK extradite anyone for either of those. On the other hand, from a quick search it seems Spain has extradited men for sex with girls between 13 and 16 - perhaps on the basis "underage sex" is a crime even if the definition of underage differs.

I do object to the way my own government currently tries to stop others from using capital punishment, but currently it simply extradites on the condition that capital punishment will not apply. Not ideal: for one thing, it creates an incentive to flee across the border after committing a capital crime, for another, it's interference in another sovereign nation, which I feel is inappropriate. Not applicable here of course, since rape isn't a capital crime anyway.

"Burden of proof" is an interesting issue; the UK's requirement currently amounts to showing the same level of evidence that is required to justify arresting and charging someone within the UK, which seems about right: if there is good evidence but not quite enough to convict, they could be extradited, acquitted and then of course be free to leave again. Going to the length of cross-examining expert or eye witnesses as you would in the actual trial would be too high a barrier to set, I think.