"The laptop has a new battery."
Translation:Läppärissä on uusi akku.
Roughly put, the ending ssä tells that the battery is a part of the laptop.
You could e.g. say that autossa on uudet renkaat ("the car has new tires" – which are a part of the car) but autolla kuljetetaan ihmisiä ((the) people are transported by a/the car" – the people are not a part of the car).
Yeah, with most inanimate things the adessive -llA ending indicates "on top of", "at" etc. An exception being inanimate objects that have human or animal-like features (e.g. "Nukella on uudet vaatteet" - the doll has new clothes).
"Pöydällä on läppäri (kannettava tietokone)" - There is a laptop on the table.
"Ovella on joku." - There's someone at the door.
On the one hand I can see the reasoning of including such colloquial-ish words, because kirjakieli evolves when some terminology or words from puhekieli seep into it. Usually this happens over quite great lengths of time but in the case of technology, the vocabulary is constantly forming and it advances in a lot quicker pace than many other areas.
So in that way I understand the struggle the course authors have on the kirjakieli/puhekieli dilemma but on the other hand I agree with you, läppäri does sound puhekieli to me. There have been some words on this course that have raised my eyebrows and not accepting kannettava tietokone instead of läppäri was definitely one of them.
Akku is standard grammar and as far as I know there isn't any other word in Finnish for rechargeable battery. Similar (maybe false friends) may be patteri, more precisely lämpöpatteri, the usually large metal radiator used in heating systems and found indoors. Paristo is the non-rechargeable (electrochemical) battery. What might make this a bit more complicated is that in colloquial usage some use the word patteri when they mean paristo.
Yeah, I really agree with you on the consistency thing and I've been frustrated with some of the words too. I was rather trying to point out that in certain situations it's really hard to distinguish what is really colloquial puhekieli and what's kind of "relaxed formal" speak.