First question: People do safely use CHE's with plastic tubs by doing what you describe - cut a hole and cover it with screen.
That said, you actually can put a baby snake right into the enclosure it will live in as an adult. The key thing is to make sure that all that space is filled up with lots of appropriately-sized hides, foliage (real or fake), tubes, branches, solid objects, etc. You'll have to adjust the hides and decor as the snake grows.
Most likely, a baby you get will have started its life in a small plastic tub, and the transition to the bigger cage with all that stuff in it can be intimidating. You can make the transition easier by getting a small plastic tub and cutting a hole in the lid, and putting the whole thing into the larger cage. Then the snake can get used to the bigger space on its own terms.
In the US it's common to use radiant heat panels for the kind of vivarium that's made of wood or PVC and has sliding doors in front. In the UK (and maybe where you are too, I don't know) it's more common to use a CHE mounted inside the cage, and protected by a mesh guard so the animal can't touch it and get burned. Those cage-type guards should be fairly easy to find if that's what people typically use where you live.
If not, you can also do the same thing with a vivarium that you were talking about with the plastic tub: Cut a hole in the top, cover it with screen, and put the fixture for your CHE pointing through it.
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