Is it permissible for a woman to travel a great distance with a strange man for fear of the road, and is it permissible to accept his gifts and return similar ones?

If the man mentioned is a non-mahram, then it is impermissible for the woman to travel with him due to the potential for fitna (temptation/strife), especially if the travel is in solitude. In such a case, fitna is highly probable and the prohibition is confirmed. It is also impermissible to exchange gifts with a non-mahram in this situation, as it opens the door to fitna. The correct approach is for the woman to travel with a mahram. If a mahram is unavailable and she is in need of study, then there is no harm in traveling with a trustworthy group of women.