Oh dear Vicki, I'm so sorry.
From a practical viewpoint you can expect the cramping and bleeding to last maybe 1-2 weeks. If the pain is really bad you can get morphine from the hospital. In some cases it's just like bad period pain. You're supposed to avoid baths and swimming etc while you're bleeding as with the cervix open the water can introduce infection, also no sex or tampons. If the bleeding doesn't seem to stop after a week or so, or you get fever or discharge then get seen asap as there may be some retained bits of the placenta and you could have an infection. They may have to do a small procedure under anaesthetic (it doesn't have to be a general, you can ask for local but it won't be pleasant) to clear your uterus.
Your cycle will resume after a few weeks, you may have a period within about 2 weeks of bleeding stopping or it could be a month or so. If you feel ready to try again (which is a very personal thing) then you can try as soon as the bleeding stops. Doctors sometimes say wait 1-3 months but this is generally to give you time to recover emotionally rather than anything medical. I know I wanted to be ttc immediately, but other people want time for closure and to prepare for the possibility it might happen again. Do what feels right for you.
If this is your first mc then it's most likely just awful bad luck and there's no reason for it to happen again. It's most likely a simple genetic error in the baby's blueprint - when the construction of the baby got to the bit with an error then it couldn't continue. Genetic errors are related to parents' age, but otherwise just bad luck, but also unlikely to happen again. After 1 mc I'm afraid the doctors are unlikely to investigate, as it's so common and most people go on to have a successful pregnancy after. Only after 2-3 mc do they start to do tests.
Please forgive the brain dump of practical advice and be sure that I know that knowing your future chances of a successful pregnancy are good does not bring back the baby you've lost. When people are trying to get pregnant they want a baby, not just a blue line. Losing a baby is a terrible, empty, wrenching feeling.
When/if you do decide to ttc again there are 2 steps you can take (1) start taking the anti-emetics as soon as you know you are pregnant, to prevent future HG, and (2) early pregnancy units are often quite sympathetic to women who have had miscarriages before, and you may be able to have an early scan. You won't be able to relax though and the pregnancy can be quite hard emotionally.
Consider whether you want to do something to remember your baby, like plant a bush or give a donation to a children's charity. Get nice people around to support you (there are lots of online groups too), and try to ignore those who inadvertently say the wrong thing. You might feel bitter or awkward around friends with babies, and this is completely natural and will get better with time. I think it's best to explain if so, most people will understand.
I hope this helps. Thinking of you. xx
P.S apologies to everyone else on the HG forum for going off-topic. I have read somewhere though that there is a correlation between early mc and hyperemesis (as in people who get HG are also more likely to have a history of early mc). Does anyone know more about that?