What also comes into this is local accent, and it will be very interesting to hear what people living in very different areas have to say. I also tend to find that a northern English or some Scottish accents can help.
However, I would suggest trying 'coeur' like pronouncing cur (a snappy dog) with a slightly rolled 'r' at the end, maybe Scottish or French.
Where we live, queue is pronounced like 'que', with a little longer ending, a bit like a short cough.
As Zarathustra has said, context is very important with mer, mère and maire. These are tricky. But I would say 'mère' sounds as though it almost might have 'air' in the middle, with a rolled 'r' at the end, with 'maire' the same. 'Mer' is feminine, 'mère' is feminine and 'maire' is masculine; so it would be 'la mer', with 'la mère' and 'le maire'.
I would pronounce 'cou' like a dove's 'coo', but shorter, as though in a rush - with the 'oo' slightly cut off. With 'cul', I'd say to have the lips very pursed and say the 'u' as a very short sound. I've heard it said with the 'l' at the end pronounced in that context.
You do get us all thinking, Patf!
Life is not about waiting for the storm to pass, it's about learning to dance in the rain.