I would line the crate with chicken wire so that the leaves don't 'escape' and just fill it with leaves and leave it open. They need moisture to help the decomposing process. You could mix in a small amount of soil to inoculate them with fungi, but if swept up from the ground they will have fungal spores on it any way.

The sack needs to be free draining or you will end up with a smelly sour 'soup' and again leave open to the elements.

I agree, use the crate. Composting requires lots of oxygen and I don't think the sack is adequate, but the crate sounds alright.

You can make brilliant leaf mould using binliners, you just need somewhere to stand them out of the way. Just fill up a binliner with damp or wet leaves (wet them if they're dry), tie the top shut, poke a few holes in the bottom and stack them somewhere out of the way. Preferably not on paving or concrete because you can get run off from the bags which may stain...

I also do that bamboo and works brilliantly, unless ivy finds a way in then they grow and use it all up !!

Yes and yes. In the past I used to use open wooden bins until they eventually rotted away and now use builders bulk bags. Both have worked very successfully for me. Leave the top open so that rain can keep the leaves wetted, excess water will drain away through the seams at the base of the bag.