Welcome to the forums, Simon.
Please ask only one question per thread. You'll get quicker answers that way.
I'll deal with the first question.
The fastest land animal is actually the cheetah, so if you want to know whether lions can run faster than tigers (or vice versa), say 'Which (animal) can run faster – a lion or a tiger?' or 'Which (animals) can run faster – lions or tigers?' (The words in brackets can be omitted.)
Note that you need 'faster', not 'fastest' when comparing two items.