After 3 miscarriages you qualify for recurrent miscarriage testing. You probably won’t qualify for NHS IVF without having these tests due to having conceived. They need to work out whether IVF would be the correct treatment for you.
I've had 4 natural pregnancy losses (2 MMC and 2 Ectopics) and was entitled to IVF on the NHS. As long as you don't have any children you are entitled.
Not necessarily, the first port of call is fertility testing. After 2 miscarriages you should be referred to an early pregnancy unit who can give you medication to support a pregnancy.