**In terms of writing styles and structures:**  
  
In order to aid ... >> ... would make more sense this way. For that same sentence, I suggest breaking it the "but.." part to another sentence. *Eg: In order to aid their poor counterparts, wealthy nations frequently provide financial assistance. Yet/However, poverty issues persist*. This way the essay has a more succinct and decisive tone (of course this is purely style preference :D).  
  
"There is a belief" is a roundabout way of writing, so I recommend "Some argue" or "It is argued."  
  
"This essay will expand ..." >> Because this is your thesis statement, so I suggest adding your subpoints right in this sentence to make your thesis complete. For eg, you can say "This essay wholeheartedly concur/agree with this argument because more developed countries have both moral duties and benefits in aiding less developed nations." "more/less developed countries" are common academic terms in replacement of First/Third World or rich/poor countries. I will always recommend writing your thesis sentence in this format: **your opinion + reasons**. Think of your thesis statement as the one sentence to summarize your essay, so that one can read that one sentence and still know your basic argument and reasoning. That will make a strong thesis sentence.  
  
"a morally right thing" >> too informal. Moral obligation is a really paraphrase you used. I'd also try phrases like moral justice/morally just, it is expected of an ethical person to, universal moral codes, etc  
  
"I think the same works" >> The same principle can apply to.... Also, I suggest you not use "I think" because it's rather informal. If you want to use that structure, "I argue" will work better.  
  
"[...] Eastern Europe to a higher development level.  
  
Finally, a point of further recommendation-- your essay will be much stronger if you can refute a counter-argument (which can be your 3rd idea). So basically you state one reason why people may argue differently from you, and why you think that is wrong. For eg: Some may argue that developed nations also have domestic poverty issues and should focus on their own countries instead of others. However, [insert your 3rd reason]. This is not essential/necessary IELTS, but can strengthen your content quality in any academic writing context.  
  
**In terms of ideas:**  
Your two reasons are good, but does not answer the prompt directly. They answer why you think more developed countries should aid less developed ones, not why you prefer other non-monetary assistance forms.  
  
One major reason why monetary aids have been ineffective is corruption -- each level of the bureaucracy put some money in their pockets and so the aid is scant or completely gone by the time it finally reaches the people/projects in need. Many donor nations handle this by requiring stronger monitoring of where money goes (which, I assure you, costs donors $$$ haha), or simply sending non-monetary aids like human resources or whatever people actually need (food, book, bikes, etc depending on the projects). Or donors can also give financial aids directly to projects they trust instead of giving to the government. Note that either government or project operation teams, how they spend aided money can be tracked to an extent, but ultimately they need some flexibility because they probably know better than donors where aids are needed the most. In a way, this is very much a trust issue.  
  
Another issue is that many people, when receiving financial aids, may not use the provided money for what they said they were going to spend on. So instead of paying for books and school, they may buy a smartphone and internet access and play games all day. Giving them book, and paying directly tuition (and tuition only) in this case ensures people don't misuse financial aids.  
  
This prompt reminds me of the micro-finance hype, where donors "loan" poor families some 'seed money' (low-to-no interest) so these families can start their own business and build up their own financial strength. Then they have to pay off their "loan" at a certain deadline. Feel free to search this up.  
  
Hope these helps with ideas for your essay.