Universities should allocate the same amount of money to their sport activities as they allocate to their libraries. Do you agree or disagree?

Your essay has several confusing sentences, where your meaning is unclear.
You mix advantages and disadvantages of the modern medicine in one paragraph when you should divide them – have advantages in one paragraph and disadvantages in another.
If you agree with the statement, you should have 2 paragraphs supporting your opinion and one supporting the opposite opinion, in your essay it is 2 against and 1 for.

3. 
   Boys are most influenced by their fathers and girls are most influenced by their mothers. Do you agree or disagree? Use specific reasons to support your opinion.
   

It is true that nowadays parent have a great influence over the children. Some people hold the opinion that the same sex is the major determination of influencing parent, but others have a negative attitude. As far as I am concerned, I agree that boys are most influenced by their fathers and girls are most influenced by their mothers. My arguments for this point are listed below.
First of all, a father is the person who have already passed that ways which are his son is passing now, in other words, sons are following their father’s footsteps. So, based on experience it is easy for a father to notice his sons’ drawbacks and to influence them.
Secondly, it is true that a boy is countedas a strong characteristics human , but a girl is a subtle and fragile one. It is hard for mothers to influence their sons, because it is not likely that vulnerable something can affect a strong one.
In conclusion, it seems to me unfair that boys are most influenced by their mothers. Based on at least two points above I strongly agree that children are influenced by a parent of the same gender.
This essay is too short, 190 words instead of the minimum requirement of 250. It doesn’t say anything about girls being influenced by their mothers, which is also a part of the task – therefore the task is only partially covered. The sentences are not complex enough, there are grammatical mistakes and inaccuracies (see comments underlined in blue). Overall, this looks like a Band 5.5 essay

3. 
   Some people believe that having a pet such as a cat or a dog helps old people to live a more enjoyable life and to stay healthier. How do you think old people benefit from having a pet? Do you think there are any problems related to old people who have pets?
   

Pets have become far more familiar within mankind community, and indeed, the importance of relationship between human beings and their pets has been proved to be slightly exaggerated in some nations. However, although problems regarding animals’ hairs may affect the health conditions of old people, the benefits that these lovely animals bring to them, physically and mentally alike, are clearly undeniable.
In term of physical benefits, the well-being conditions of elderly people with pets are more favourable compared to those without pets, since not only do they have to take care of themselves, __ the responsibility that ensure their love one being fed and well looked after encourages them to become even more active. Due to these extra activities, this though might not have an obvious influence on their health, but at least this could help them to avoid bad living styles. Coupled with physical side, their mental wellbeing will also be improved, and the reason is that having someone to take care of would reduce the chance of feeling loneliness. Therefore, their depressing rate could be minimised.
In spite of the above advantages, the threats of too close interaction between pets and vulnerable old people still exist. One of the major concerns is the harmfulness of these animal hairs on their tracheas, especially those with asthma. Because of the virtually invisible in the air, many asthma symptoms are caused unconsciously by pets. In addition to the fact that old people might experience difficulty in looking after their pets, as their health conditions are limited, which could become even more challenge when they try t take care of others.
In conclusion, it is true that obstacles still exist for elderly people in adopting pets, but the benefits of this topic outnumber its shortages. For such reasons, instead of discontinuing them, further support would be far more beneficial.
You have made an attempt to accomplish the task response. However, there are quite a few mistakes in the essay – the main problematic areas are grammar, sentence structure and word choice. In addition, the length of the task response could be reduced. This task response needs to be worked on and improved. Revise grammar and work on your sentence structure. Avoid writing more than 280 words to save time and reduce the number of mistakes, and remember to always proofread your work once you’re finished. Overall, this looks like a Band 5.5 essay