Yes you can get DLA without a diagnosis as it is based on care/mobility needs rather than the diagnosis itself
As long as you have evidence to show that you have difficulties and need help with what you have put on the form then it should be fine. It is getting harder and harder to get, but I wouldn't be put off because a lot of people are turned down at first. Yes it really is emotionally draining and challenging, it plunged me into a rather nasty depression doing that form, but it is worth it because we can afford stuff that I need to help me cope and it passports onto so many things!
Hang in there
J - 28,student,married to the lovely Em and live with 2 cats Bilbo and Pippin. Diagnosed with Aspergers, Dyspraxia, Dyslexia, EDS-HM, Mild Asthma, Chronic Pain, Chronic Fatigue, POTS, Syncope