Can I just help only one Torah institution? I once heard that one can not and that one should diversify his maaser money. Is there a halacha forbidding to help only one institution?
Yes there is such a halacha, that one should not give all of his maaser money to one place, so others that also need will be able to get. It even applies to a person supporting his relatives, parents or his rebbi etc. Therefore it will surely apply to supporting an institution.
Eruvin 63a, Mordechai Baba Basra 52, Tosefos Kesubos 26a D:H Aiyn, Y:D 257-9, Shach 257-19, Igros Moshe Y:D 1-144.