How is monetary policy fair in the current economy? I've just read Money Creation in the Modern Economy, an article published by the Bank of England.

This article brings about a lot of questions in my mind. This article talks about money being created through commercial bank loans, and that central banks only have the authority to set interest rates or to employ quantitative easing in order to stimulate the economy. Loans being repaid should theoretically destroy the money that was created and balance the books, but inflation grows in that economy as banks earn interest (and in this case, the interest is actually the money that never existed, assuming that they destroy the rest of the money paid back).

So, my questions is:

How is this fair for every other constituent in the economy who has earned money the hard way, by working and not by generating it so freely like interest returns on loans do for commercial banks?

How is inflation fair, as populations increase and every time someone gets a bank loan, new money is added to the economy over time as they pay back that loan, and everyone else's currency is de-valuated?

Consider country X which has one constituent named Roger who works at a commercial bank in X and, coincidentally is also the president of X. He gets a loan from his bank for 100 dollars (with an interest rate of 5%), however, in his economy, only 100 dollars of money exists as actual currency and he has 0 dollars in his bank account. He will never be able to pay off his interest rate of 5% without getting another loan. His bank or state will coincidentally not be able to pay him his wage over time without printing new money from a central bank or giving his bank a loan, or, perhaps a bail-out. All this interest will do is inflate the economy, and you can only fight interest with interest.

Now apply this concept to our current economic system on a macro level, and it feels to me like it will ultimately fail as a system, because inflation can only combat inflation for so long until the price of every asset reaches infinity.
The description you're providing of how interest works is based on a couple of fairly common misunderstandings about how the system actually works, so lets clear that up first.

Fractional reserve banking and the gold smith banking systems preceding it, are a result of the development of an accounting technology called double entry book keeping in the 13th century.

Double entry book keeping grossly simplified. Each transaction must consist of a debit and a credit tuple, occurring in two separate books. Asset books are traditionally written on the left, and liability and equity on the right. On the right hand side (liability and equity side), credit adds, debit subtracts, and its the opposite on the left hand side, debit adds, credit subtracts. Just remember the right hand side is what you think it should be, the left hand side is the opposite.

When a bank makes a loan, it performs the book keeping operation:

[debit loan, credit customer account]. 


This creates the loan, and it creates money in the form of the matching deposit. When  loan capital is repaid, the operation is:

[credit loan, debit customer account] 


and this removes the deposit money that was created.

So how does interest get paid? Well in your example, Roger gets a loan for 100, lets say it's a 10 month, simple interest loan (easier math.)

The first month, Roger repays 10 capital, and 5 in interest. That's:

[credit loan 10,        debit Roger account 10]     

[                       debit Roger account 5, 
                        credit bank interest income account 5] 


The bank's interest income account is also classified as a liability, although not strictly as a deposit account. Once the bank has recognised that income, it can then use it to pay expenses. Let's assume Roger works for the bank, and the Bank pays Roger a monthly salary of 5. That just reverses the operation above, ie.

[                       debit bank interest income account 5, 
                        credit Roger account]


The next month, Roger pays another 10 in capital, and pays 5 interest, and gets the interest back in salary. This continues until the loan is repaid. 

The key concept is that in an economy, money is exchanged and individual units of money are constantly circulating through the economy and being re-used, as in the example above. It's a flow system essentially, and this applies to interest payments just as much as payments for food, etc.

Money in a fractional reserve monetary system today also predominantly takes the form of liability bank accounts, rather than physical currency, and most banking operations these days operate as transfers from bank account to account. The writers who concentrate on physical currency in describing this system seem to miss this point, and consequently get key points incorrect. 

This doesn't mean that there isn't a very challenging accompanying inflation problem. Generally over time, banking systems tend to create more new loans at a slightly higher rate than they are repaid, and so the system is in a more or less continuous state of growth. There's no reason why it couldn't be regulated to be stable - but the problem is nobody at this time knows what that would do to the economy. The best guess at the moment is that a low but positive rate of expansion is optimal.