Question: is it allowed for a father to distribute his property without referring to the ratios as indicated in inheritance in Islam?
Answer: In court, unless he was sick while giving, yes. However, in terms of the religion (whether he has committed a sin or not) if the gifts are to his sons, and he gives different amounts to them, then there must be a reason for this, such as giving more to those less able to make it on their own (e.g. due to disability). Otherwise it may cause frictions and jealousy between them. If the gifts are to other inheritors, then he gives as he wishes.
An exception in court would be if these gifts were given while he was sick from a sickness that kills, in a way that prevented him from doing his usual work, and he died from that sickness (within a year). In this case, in court, his gifts are considered part of his testament, and can amount to no more than 1/3 of the total inheritance.