I do sympathise with the bizarre thoughts thing. I used to have to pass the top of our (steep) stairs en route from the bathroom to dd's bedroom, and every single time, for about the first 4 months, when I had her in my arms I used to imagine her falling down the stairs. I tried not to think too hard about it each time, as I was convinced I was about to involuntarily throw her down them. Sort of how you get when you're on top of a very high building - you imagine you're going to jump, even though you almost certainly won't. The feeling did pass eventually, but I still occasionally have the same thoughts when at the wheel of the car, when passing lorries or brick walls that I might crash into.
I also used to wake up in a sweat every night, imagining I'd overlaid her in bed - patting the duvet frantically until dh woke up. This was despite never ever having fed her in bed (precisely because I was so worried about this!).
I think our fears in the early postnatal days are because all of a sudden we are in such an incredibly responsible position. We're reminding ourselves of how fragile the baby is, and how, at this point, their survival is in our hands. This is really really daunting!!!
And in a way, because with the second child we have moved on, the child has grown and developed and the responsibilities have changed, we've forgotten what it is like to have that small thing so entirely reliant on us. I think fears about the baby in this kind of situation are entirely normal.
It sounds to me like your dh is having the same fears, except that he is expressing them by expecting you to sort out things like her crying. Instinctively, because you are the mum, you are assuming that you have to do this yourself, but I agree with the earlier post - he could help. Can you perhaps explain how you're feeling to him, and ask him if he's feeling the same way? It might make it easier to persuade him to give you some time to yourself, which you sound like you need.
This may also explain the sex thing. I remember my dh being really keen quite soon after the birth (he also suggested that I cycle down to the chemist to get something the baby needed, 2 weeks after having given birth, but that's another story!!). I think sex in this context is being used as a way of him feeling like things are back to normal - ie as they were before the baby was born. He's probably mourning the loss of your previous life too.
I found I had to explain to my dh (who is, despite the cycling incident, a very very switched on man), that I needed time to myself, to do something really frivolous. We reached an agreement that he would look after the baby for say 2 hours on a Saturday, but only on the express proviso that I went shopping, or sat in a cafe and read the paper over a coffee, or something 'non-productive' like that. His giving me 'permission' to do something other than getting a household chore done, was what I needed to make sure I didn't feel guilty about enjoying myself. We've tried to maintain this (as I speak he's currently skiing for a week in France at my insistance - I am expecting no 2 in 3 weeks' time, but know I can count on similar levels of support after no 2 is born).
I do hope you feel better soon. If it's any consolation, I am truly worried about how I'm going to feel when no 2 is born. I love routine, and am terribly structured too, plus there's going to be a 3 year gap between the children, and I have always been a child, rather than a baby person. So I shall be really interested to hear how you get on, as I think I'll need some inspiration from you in a few weeks' time!