Hi,
I noted down some grammatical problems that you may want to change:
It is an irresistible trend that nowadays, co-operation between eastern countries and western countries is becoming stronger and stronger, creating hundreds of studying abroad opportunity to eastern students.
I don't really see how the first part of the sentence can link with the second part. Anyway, to make the sentence more succinct you can just shorten it by saying "stronger cooperation between... creates ..."
Instead of enjoying the comfort of living in their house, many courageous students decide to study in different foreign countries where they have to organize their lives independently, for instance, cooking on their own or working hard for single pennies.
I think you can just say foreign countries to avoid redundancy
Accordingly, students will be equipped with many valuable qualities such as independence, initiative and especially adaptation, which would be perfectly vital for overcoming numerous challenges in their lives.
You may want to change 'accordingly' to another linking word like 'As such', because 'accordingly' means something like 'in a suitable way'.
for overcoming--> to overcome
The main drawback of it is, in my opinion, it imposes financial burden on students's families.
Overall, I think your essay is quite interesting. Do proofread after writing to avoid grammatical mistakes though, and you will be fine :) All the best!