Usually you can only save until a certain baseline level, then you'll need more income. If you really can't afford your rent plus + utilities, you need more income, now.
In this post I use $ but that is because it is easiest to type on my keyboard. I think what I say is pretty universal.
While a $25/week food budget is possible on a very short time frame, you'll find out that food is pretty expensive and expecting that little expenditure is unreasonable. What is inevitably going to happen is you are going to make a big plan, and get to the store and items A, B, and C are 200% of the price you were expecting.You either don't get the items, and end up with absolutely bare bones meals for the week, or end up spending more and throwing off your budget.
That being said, food is the easiest to control living expenses. No snacks, keep things as basic as possible. There's a huge world of easy to find information on this out there.
As far as entertainment budget, if you seriously don't have the money, then this needs to be $0 until you get more money. Unfortunate fact of life. If you get said amazon voucher, you should sell it to one of your friends or a random person for as close to par value as you can get. The library is still free almost everywhere, and the internet has more entertainment for free than anyone could consume in a lifetime.
Liquid dish soap (not dishwasher-machine soap) is extremely harsh to use in long term but is extremely cheap, and can be used for ordinary hand soap, body wash, and shampoo. A little goes a very long way since it is so concentrated. It also does as good as many other household cleaners.
Laundry can go a lot longer than you think without washing.