Point 3 is the least of your problems. You can have millions of pounds in the account but if points 1 and 2 are not overcome, then it will all come to naught.
Point 2 can be overcome with the sledgehammer approach, as distasteful as it is. Overwhelm them with copies of letters, emails, phone logs, photographs, etc.. to the point that they can't say that the relationship does not exist.
Point 1 is the most difficult one to overcome for most "third world" applicants. She will need to show secure employment and/or solid ties to Azerbaijan - no real way around it short of being an EU dependent. The absence of either employment or ties raises the burden of proof for the other. A prior refusal also makes things harder as there is now a finding that the existing situation is inadequate - so you MUST provide new evidence that further substantiates her financial situation and ties in order to overcome the refusal.