Furthermore growth of technology is counted as new reason of carry out crime, for example, Internet is new definition that related to stealing money via the Internet.

Correction: I would suggest using a comma after "furthermore"

Correction: "The spread of technology" or "the growth of technology"

Correction: Instead of "is counted" (counted by whom specifically), saying "could be considered" or "may be considered" sounds" a tad better, especially since you are not citing specific data or people

Correction: "for the rise in crime", not "of carry out crime". 

Correction: I am not certain of your meaning after "for example" . I would suggest making this a new sentence and end the previous sentence with a period. 

Correction: No need to capitalize "government". Also, I would suggest making it plural, unless you are referring to a specific government (in which case, mention which one).

Correction: "improve citizens/people's economic situation"

Correction: "non-return"

Correction: "lien" not "lean" (they are valid English words, but have different meanings"

Correction: Make "subsidies" plural 

All these action actions can help to have  create adequate (or "sufficient") income to cover their poorer citizens' financial problems.

Correction: I would consider using a synonym for "problems", such as "concerns" or "worries"

Moreover, education always plays a central role in decrease the rate of crime, for example if people have enough information about how to use the internet for checking their bank account or buying online, they are rarely being victim of illegal internet actions.

Correction: Put a period before "for example" and create a new sentence

Correction: "They may be less likely" instead of "they are rarely" (we want to use "may" because you aren't mentioning specific data or research)

Correction: I would suggest "Online crime" or "illegal activity online"  instead of "illegal internet actions"

In conclusion, there are many factors that ("may" or "can") impact on (the) growth of crime and make our life a bit miserable. To face with all these factors, both government(s) and people ("citizens" sounds a tad better) should collaborate with each other (mention an outcome)

Correction: "Make our life a bit miserable" is a tad hyperbolic". you may want to say something along the lines of "making our lives more difficult"

Correction: "To face" means "to confront" or "acknowledge". I believe that you mean "to solve", so you may want to say "to solve", "to alleviate", "to address", etc. 

Correction: I would say "to address/solve/alleviate these issues" instead of "these factors". You could also say "these contributing factors"

Correction: "There are several causes . . . "

Correction: I would suggest using "given rise to" or a similar phrase; "lain" sounds a tad unnatural. 

Correction: "To begin with" is typically used at the beginning of a sentence, not the middle

Correction: You may want to say something such as "among which, economic inflation is . . . "

Correction:  Do you have data to back up that data is the "core of all criminal activities"? If not, you may want to make the statement a little softer, such as "I believe that ..." or "among which, economic inflation is arguably . . . "

Currently, cost of living is rapidly increase, that’s why many people are struggling to cope with their financial issue, For instance, some occasion they have to committee a crime such as rubbery to handle their needs.

Correction: is "rapidly increasing" or "increasing rapidly", not "rapidly increase"

Correction: In writing, we generally want to avoid using contraction. It may be better to say "which is why/which may be why ..."

Correction: I would suggest saying "Their financial issues", and rather say "their respective/various financial issues."

Correction: After issue, use a period, not a comma. 

Correction:  "On some occasions" or "in some instances", not "some occasion"

Correction: Not at all people will commit crimes to solve their financial problems. You may want to say something like "some people have gone to such extreme lengths as to commit a crime to meet their financial needs"

Correction: I understand what you mean by "handle their needs", but "meet their (financial needs)" sounds a tad more natural. 

Correction: "Robbery" refers to the act of stealing something; "rubbery" is an adjective meaning "rubber-like"

Secondly, the growth of consumerism is another important factor. As this phenomenon causes people to have a strong desire to buy new stuff despite of having adequate income to cover all their cost.

Correction: Using "secondly and "is another important factor" together sounds a tad wordy and redundant. Saying: "The growth .... is a second important factor" or "In my opinion, the second major factoring affecting  . . . . . is the rise in consumerism"

Correction: You may wish to combine these two sentences into one. 

Correction: I would say "items" or another noun, "stuff" is too informal. 

Correction: You can say "in spite of not having . . . " or "despite not having  . . . ", but not "despite of"

Correction: "all of", not "all"

Correction: You could say "costs" (plural), but saying "covering their cost of living",  "basic expenses" , living expenses, etc. 

I will correct the third part soon. 

In many countries the amount of crime is increasing (IELTS writing).

Correction: Remember here that the upside question mark is not used in English writing. 

Since the beginning of time, committing crime has always been calm of humans

Correction:I'm not sure what you by "calm". "Calm" refers to there being peace or no conflict.  It mind be better to say that "committing crimes have always been a part of human nature" or "committing crimes has always been a part of human societies."

Nowadays, in many nations committing offence is on the rise and should be taken seriously. I think that there are two reasons behind criminal activities along with remedial step to resolve this problem.

Correction: "Nowadays" is a  a tad informal for writing, you may want to use "In recent years", "recently", or something similar. 

Correction: "Committing offence" isn't the most common collocation/phrase that you could use. It may be better to say something along the lines of "crime rates" or "rates of criminal activity". 

Correction: I understand what you mean by "taken seriously", but doesn't quite sound as formal as one would say in writing. We could say "deserves immediate attention/action" or "ought to be considered a serious concern" or "ought to be addressed swiftly", or something similar to those. 

Correction: "I believe" or "in my opinion" are both better phrases to use in writing than "I think". 

Correction: There are obviously many reasons behind crime rates. It might be better to say that "there are two main/primary reasons" than just "there are two reasons"

Correction: Instead of "along", you may want to say "that can be resolved by . . . ".

I will correct the second part of your essay soon.