I have nothing to do for now.
Is correct.
Nothing for doing for now.
Is incorrect.
I have some things to study.
I have some things for studying.
Both are correct. I will explain.
Using '-ing' is a common problem because it has more than one usage in English, and in other languages it doesn't (Spanish, Portuguese, etc.). For your sake I'll compare it to Portuguese because you're from Brazil.
Here are the two ways you could use '-ing':
1- I am running. ("Running" is a conjugated verb. "Correndo" como "Eu estou correndo". A conjugação chamado o gerúndio.)
2- Running is a great sport. ("Running" is a noun that refers to the activity in general. "A atividade de correr" como "Correr é um grande esporte". Aqui, não é um conjugação ainda que tem '-ing'.)
Those are the two ways we use '-ing' in English, which is different than Portuguese.
In English, you can only use 'for' + '-ing' with the second usage of '-ing'. That's the reason that...
I have some things for studying.
...is correct. "Studying" here is a noun referring to the activity in general, "A atividade de estudar".
The sentence...
I have some things to study.
...is also correct. "Study" here is a verb, "estudar".
Nothing for doing for now.
...is wrong for many reasons. First, because it's missing a verb. Second "For doing" is correct, but no one uses it alone like that, and so it seems very wrong to us. Never use "for doing" alone. Only if you will say something like "for doing homework". I imagine you wanted "There is nothing to do for now".
Now, I will explain the difference between 'for' + '-ing' and 'to'.
'For' + '-ing' means 'For the purpose of... ____-ing'
You will use this when you will follow it with a noun '-ing' word (or a noun phrase).
'to' simply means there's a verb after it.
You will use this when you will follow it with a verb (or a verb phrase).
Final note 'For'+'-ing' is rare, and because of this, it sometimes sounds awkward (esquisito). So only use it if you know it's correct the way you will use it. Otherwise, use 'to'.
Hope that helps.
-ing
form of a verb is also known as thegerund
.for
withfor the purpose of
- I now rescind this recommendation because this is not a comprehensive nor definitive test, as can be seen in the examples offered in my answer below.