There are a couple of things wrong with "It rains a lot into those lakes".
The Hungarian sentences is about the amount of rain, but "It rains a lot" usually means that it rains often. Also, to my ears, "It rains ... into those lakes" sounds awkward and unnatural. I much prefer the given translation, "A lot of rain falls into those lakes."
I am only at Level 13 from English to Hungarian and at Level 16 from Hungarian to English, which I started first. Hungarian is a lot more difficult for me, than English, French and Italian, in which I reached Level 18/19 quite easily, without great effort or time. I went quickly through the Beta Hungarian version and finished the tree at Level 12, but at that point a fluent conversation is not yet possible and while exercising again and again, my progress still dissapoints me often. My problem is mainly, that I could never (in any language) remember the rules, cases a.s.o. I am impressed by the knowledge and linguistic understanding of some people here, who helped me a lot, when I was stuck to catch it only by intuition. Yes, I want to encourage you to go on, like others encouraged me too, or at least understood, when I was about to quit. It is a great challenge to learn Hungarian and at the moment I do not need another one. Be proud, that you already reached Level 9.
It seems like liquids usually go "into" other liquids. Well, as long as they mix.
- pouring milk into coffee
- spitting into a lake
- there are solvents in this river
- pumping waste into the sea
- there is oil in/on the lake (surface)
If your lake is frozen over, you can say that rain falls "onto" it, though.