Corrected version:

The 21st century has witnessed a significant increase in the number of opportunities for studying abroad.

Explanation: 

Changed "to study" to "for studying" to match the correct preposition "for" that should be used with "opportunities."

Improved version:

The 21st century has witnessed  an unprecedented surge in opportunities for individuals to pursue education abroad. This remarkable phenomenon is shaping the global educational landscape. 

Corrected version:

This essay will shed some light on the upsides and downsides of this statement. 

Explanation: 

Changed "behind" to "of" to correctly indicate possession and relationship.

Improved version:

 This essay endeavors to explore the intricate tapestry of merits and demerits underlying the aforementioned assertion. By dissecting these facets, we can gain a deeper understanding of this complex issue.

Corrected version:

On the whole, a growing number of people indulge in shaping their lives and fulfilling their materialistic needs, which are major contributors to the prevalent issue as pupils go abroad for further studies.

Explanation: 

Corrected verb tense from "indulged" to "indulge" and corrected spelling of "prevalent." 

Improved version:

Overall, an escalating number of individuals are actively engaged in shaping their lives and fulfilling their aspirations for material gain. This conspicuous trend has a profound impact on the prevalence of students choosing to seek education abroad.

Corrected version:

In today's globalized world, a significant number of students go abroad, but in the past they pursued a university degree in their own nation. There are many upsides to studying abroad. 

Explanation: 

Removed "the" before "significance," corrected "number of students go" to "a significant number of students go," restructured the sentence for clarity, and corrected the expression to "upsides to studying." 

Improved version:

In today's era of heightened connectivity, a substantial portion of students opt to pursue their studies abroad, a stark contrast to historical norms where education was primarily localized. This shift prompts an exploration of the manifold benefits associated with international education.

Corrected version:

Firstly, pupils can explore the world in a better way; they can learn about different cultures and traditions, as it is paramount for people, and they can encounter greater opportunities in their lives.  

Explanation: 

 Added "a" before "better way," split the sentence for clarity, added "can" before "learn," and corrected "meet a greater opportunities" to "encounter greater opportunities."

Improved version:

Primarily, students embarking on global academic journeys are enriched through immersive cross-cultural experiences. Gaining insight into diverse traditions and lifestyles cultivates a broader perspective, nurturing a tapestry of opportunities that extend far beyond academic horizons.

Corrected version:

Secondly, if they study abroad and get job opportunities, then pupils can earn income. 

Explanation: 

Added "they" before "study," corrected "in abroad" to "abroad," changed "get" to "can earn," and added "can" before "earn income."

Improved version:

Secondly, by embracing the prospect of international education and seizing lucrative job opportunities, students can tangibly bolster their financial prospects. This economic empowerment contributes directly to elevating their quality of life. 

Corrected version:

Furthermore, it enhances the living standards of pupils.

Explanation: 

Changed "standard" to "standards" to match the plural subject "living standards."

Improved version:

Furthermore, the pursuit of education beyond borders isn't merely an academic endeavor; it catalyzes an overall enhancement of students' living standards. This encompasses aspects ranging from personal development to societal contributions.

Corrected version:

Turning to its drawbacks, in the current pace of life, a significant number of pupils are suffering from many problems while they study abroad. 

Explanation: 

Corrected "it's" to "its," added "while" before "they study," for clarity and proper conjunction.

Improved version:

Transitioning to the potential drawbacks, within the accelerated pace of contemporary existence, an appreciable cohort of students confronts multifaceted challenges in their pursuit of education abroad.

Corrected version:

This means that they lose their family relations as well as suffer from depression.

Explanation: 

"Meaning that" with "This means that," corrected "loss" to "lose," removed repeated "they," and corrected "suffering" to "suffer."

Improved version:

This predicament often precipitates strained familial bonds and psychological distress. The paucity of avenues for emotional expression exacerbates this situation, becoming a pivotal catalyst in the dynamics at play.

Corrected version:

If folks cannot share anything with others, for instance, it becomes a significant driving force behind this issue. 

Explanation: 

Corrected "stands it" to "it becomes" for proper verb agreement.

Improved version:

In cases where individuals find themselves unable to articulate their thoughts and feelings to peers and mentors, the impact of challenges during their international studies is markedly magnified. This underscores the urgency of effective support systems. 

Corrected version:

Financial burdens have become an indisputable problem for overseas pupils. 

Explanation: 

Corrected "Financially burden" to "Financial burdens," added "an" before "indisputable," and corrected "problem" to "problems" for plural agreement. 

Improved version:

Beyond the realm of academics, the formidable financial burdens faced by international students have surfaced as an undeniable impediment to a well-rounded education.