All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
There is no doubt that what this organization is doing, i.e. helping the needy, taking care of the children and homeless people is within the good moral standards and manners that religion urges people to do.
It is confirmed that the Prophet said: "Whoever facilitates things for a person in hardship and difficulties, Allaah will facilitate things for him in this worldly life and the Hereafter." [Muslim]
There is no harm, Allaah willing, in the prizes that are given to the donors for this organization, if their intention, when donating, was not to get a chance for the draw.
However, if the motive for such donation is in order to obtain a token for the draw, then, in this case, it is not permissible and this is pure gambling.
The prize of the winner of the draw, if the draw is carried out in a permissible manner, is lawful money, and it is permissible for the winner to benefit from it.
However, a Muslim should not seek a worldly reward when making a donation, because even if he is not sinful for this intention, he may not get the reward for it from Allaah.
Some righteous predecessors interpreted the saying of Allaah: {And that which you give in gift (to others), in order that it may increase (your wealth by expecting to get a better one in return) from other people's property, has no increase with Allaah,…..}[Quran 30:39]; that it means the gift that one offers to get worldly reward. The winner of such a draw should donate the prize as well.
Lastly, it should be noted that whomever Allaah has guided to Islam, it is not permissible for him to affiliate himself/herself to non-Muslims. A Muslim should also volunteer and work for Muslim charitable organizations, if any, as it is more appropriate to donate and work for these Muslim organizations than for non-Muslim ones.
Allaah Knows best.