Yucca - This can be prepared many ways. First you need to peel off the waxy skin. Best way to do that is take a butcher knife and chop into the Yucca lengthwise and peel up the skin and then keep it going all the way around. Once peeled, you can boil it, boil it then fry it, grate it to make little fritters, chop it in big chunks and add to sancocho or soup, etc.
My favourite way to eat it is to peel it, then cut into about four inch chunks (length-wise) and then cut in half length-wise so you have a bunch of half-round, four inch chunks. Boil with a bit of salt and when you see it starting to break apart but with a fork inserted is still semi-firm, it's done. You can then eat at a side dish with a variety of prepared meats, fish, etc. It's really yummy if you prepare something "guisado" and have some liquid to mix it with.
You can also cook as above and then drain and deep fry for a minute or two. Remove from oil and add a bit of salt.
You can add to any soup or sancocho and boil in about 2 inch chunks.
I especially like it with bacalao guisado or just plain on the side with some red onions cooked with vinegar and oil or with some lambi, cold with onions, vinegar and peppers.
For fritters, you need to peel, pat dry, add salt and a bit of egg and then form little patties and fry. Lightly salt when done.
I used to hate yucca - now it's one of my favourite foods.
As for the "pumpkin-like" squash... you can chunk it up and add to habiscuela guisado, habiscuela (sp?) con dulce or add to sancocho. In North American style cooking, you can also make a creamy soup out of it like any other squash or bake and scoop out flesh, mash it, add butter and salt and serve.