One of the important principles that the Qur'an teaches its followers is to try for good that is under your control, to be eager in attaining good qualities within your ability; not to fall behind the things beyond your ability, not to try for what is beyond your power. The Quran refers to this teaching in this verse-

وَ لَا تَتَمَنَّوْا مَا فَضَّلَ اللهُ بِهٖ بَعْضَكُمْ عَلٰی بَعْضٍ لِلرِّجَالِ نَصِیْبٌ مِّمَّا اكْتَسَبُوْا وَ لِلنِّسَآءِ نَصِیْبٌ مِّمَّا اكْتَسَبْنَ وَ سْـَٔلُوا اللهَ مِنْ فَضْلِهٖ  اِنَّ اللهَ كَانَ بِكُلِّ شَیْءٍ عَلِیْمًا.

Do not covet something in which Allah has made some of you superior to others. For men there is a share of what they earned, and for women, a share of what they earned. Pray to Allah for His grace. Surely, Allah is All-Aware of everything. Surah Nisa (4): 32
Allah, out of His infinite wisdom, made some people superior to others. He made some of them superior to others in various qualities. Someone is wealthy, someone is poor, someone is physically beautiful, and another one is less beautiful. Someone is blessed with children. And another one is not given the children. The variation of being rich or poor, beautiful or unbeautiful, strong or weak, healthy or sick is nothing but a special manifestation of the wisdom and power of Allah.
Why is this difference between rich and poor? Why is this difference between strong and weak? Behind this diversity there is a great wisdom of Allah. Scholars have tried their best to analyze the matter. Many important issues have been discussed in this analysis. But the reality is that it is not possible for any human being to completely reveal the mystery of Allah behind all his decisions. And believers do not need to know it. Because we firmly believe that all the decisions of Allah are good for us. Therefore, we do not need to know the wisdom hidden in the work of Allah. A believer is not the slave of wisdom and mystery, rather a believer is the slave of Allah. He is always ready to accept any decision of Allah from his heart.
In this verse, Allah has given us a decision along with some instructions. Allah has made some people superior to others in some qualities that are beyond man's control. For example, Allah made some woman beautiful and another woman more beautiful. Now the former should not feel jealous of the latter. The former should not say, I wish I was as beautiful as she was! Because obviously it is not possible for her to be as beautiful as the latter one is.
Similarly someone was born in a noble family. Now it is not right for someone else, who was born in an ordinary family, to covet, 'I wish, I were also born in a noble family.' Because, this desire is of no use at all. Therefore it is forbidden to desire such things. 

Allah says- Do not covet something in which Allah has made some of you superior to others. There are some other qualities that can be achieved (partially or fully) through effort if Allah wills. This type of qualities is of two categories: religious and worldly.
If Allah made someone superior to others in religious qualities, such as Allah gave someone more knowledge and more tawfiq to do good deeds, then the superior can be envied and possible efforts can be made to achieve these qualities. The Qur'an and Sunnah encouraged us to be inspired by good people and to be competitive in good deeds. This verse also points to that. The verse says,

لِلرِّجَالِ نَصِيبٌ مِمَّا اكْتَسَبُوا وَلِلنِّسَاءِ نَصِيبٌ مِمَّا اكْتَسَبْنَ

For men, there is a share of what they earned, and for women, a share of what they earned.

That is, men have been given power to accumulate the capital of the Hereafter by doing good deeds. Everyone has been given the opportunity to do good deeds without making any distinction between men and women. The more good deeds a person does, the more benefits he will get in the hereafter.
As for worldly qualities that can be achieved through effort (partially or completely) by Allah's tawfiq such as wealth, the rule in this case is that a poor should not feel nervous and inferior seeing a wealthy person. However, it is permissible to earn wealth in a lawful manner and to try to increase wealth.
It should be noted that to earn wealth and lawfully increase wealth for one's own needs is one thing, and to become nervous or feel jealous or inferior by someone's wealth is another thing. Shariah allows anybody to earn wealth and try to increase wealth in recognized ways, but it does not allow anyone to feel jealous or lustful for others' wealth. This is the basic teaching of the verse. Then the verse says, Surely, Allah is All-Aware of everything.

Allah is All-Knowing. He knows everything you need. He gives you what is good for you. His grace is also varied. Allah blesses someone with wealth and ‍does not give him children. Maybe it's because he can bear the pain of not having children, but can't bear the lack of wealth. He blesses someone with children and does not give him wealth, because, children are dearer to him than wealth. He bestows both blessings on someone, because, he may be able to appreciate both blessings. In this way, different things are given to different people on different reasons. It is not possible for us to fully understand this wisdom. So, if someone else got more than what I got, there is no need to become envious for it. Allah gave it to him according to His wisdom. He provided me with what is useful for me. Allah's grace is manifested in many ways. So it is better to ask Allah for favors unspecifically. He will bestow upon me the grace that I deserve.

Yes, it is permissible to pray something specifically, keeping in mind the related usul and adab. In that case, Allah provides it in the appropriate place according to His wisdom. If it is not suitable, then he does not provide it.

Lessons we can learn from this verse-
a. Allah Ta'ala, in His infinite wisdom, gives superiority to some people over others in certain matters. Among these there are things over which man has no jurisdiction. Man's duty is to accept these decisions of Allah Ta'ala from the heart and not wish for extrajudicial matters.
b. It is not only desirable but also laudable to strive to achieve jurisdictional religious matters.
c. It is permissible to try to achieve worldly matters under the jurisdiction in accordance with shariah.