If a father-in-law is helping support his son-in-law who is learning in Kollel, does the father-in-law get reward for the son-in-law's limud ha'torah? Does it depend on how much he is giving and/or what the couple use it for?
From the source of @user6591 in comment (Shulchan Aruch Harav Talmud Torah 3.4).
sponsoring anyone to learn Torah you get part of their reward,
The Shulchan Aruch Harav's source is the tur and ramo on 246.1 where it says supporting someone's learning is like learning yourself (maybe it is only if you can't learn yourself)
ומי שא"א לו ללמוד מפני שאינו יודע כלל ללמוד או מפני טרדות הזמן יספיק לאחרים הלומדים ותחשב לו כאילו הוא לומד בעצמו כמו שדרשו חכמים בפסוק שמח זבולן בצאתך ויששכר באהליך
Brings that our sages learned it from the pasuk devorim 33.18 (see rashi there)
...Rejoice, Zebulun, in your departure, and Issachar, in your tents.
(If it was your son then you are doing the mitzvah of teaching your son Torah (hilchos Talmud Torah 1.7 see footnotes there, from 1.6 it is seen that this obligation is only until the son knows the whole Torah at once (even if he forgot it afterwards) (and that he can not do learn it all on his own)).
But by your son-in-law then it might be more complicated, since there is an idea to marry your daughter to a good son-in-law (even if it will cost you everything you have, (which by other obligations you are not required to do)), and there is a mitzvah dirabonon to give your daughter a dowry (according to your earnings, with a minimum of the amount for clothing for a year)
So then if it was part of her dowry to give your son in law money you might only get the reward for giving the dowry and not for the learning,
If you are just giving money to your son-in-law for any use (not for Torah) and it was not part of the dowry, then it might be the mitzvah of tzedoko (and you get reward for it) (part of the mitzvah is to give the people who are closest to you)
If the use that they are using it for, makes him be able to be more available to learn Torah (and he learns) then it is like paying him to learn
Does it depend on how much he is giving
I guess it is calculated by how much more Torah (time and quality) the person can learn becouse of the money given to him, But becouse some people explain that every extra moment used (without a brake) is exponentially grater so the amount of quality of the Torah is much greater, so the reward is hard to calculate, (not having to worry about feeding his family also effects the quality)
PS it will take me time to add sources so if there are parts of my answer you want me to add the sources please say so in the comments
PPS The kizusur Shulchan aruch 27.2 also brings it
...One who does not know at all how to study or it is not possible for him because of many distractions, should provide for others who study. This will be considered as if one studied oneself, as explained2 our sages, of blessed memory, on the verse3 ''Rejoice Zevulun, when you go out, and Yissachar in your tents.'' Yissachar and Zevulun established a partnership, Zevulun would be involved in trade and provide Yissachar with his livelihood, in order for him to be free to study Torah. Therefore, the verse puts Zevulun before Yissacher, since Yissacher's Torah was due to Zevulun. Similarly, we find in the Mishna4 ''Shimon, the brother of Azaryah, said..''. And (the Sages explain) that Shimon was called (also) by his brother, Azaryah's name, since Azaryah was involved in commerce and supported his brother Shimon, who studied Torah. They agreed that Azaryah would share in the merit from Shimon's Torah study. Nevertheless, everyone should make an effort to study it (Torah), even only a little, every day and every night.
2) Bereishit Rabbah 99.
3) Deuteronomy 33:18.
4) Zevachim 1:2.