Can I live in Berlin comfortably for one month with 1,000 euros if housing is free?

Yes, easily.

When I started my company a few years ago, I was living on this exact budget in Hamburg, which is quite similar to Berlin in living costs. As I was living in my own appartment, I had minimal housing costs (electricity, water, etc.). I also didn’t own a car at that time.

You can buy a bus ticket for the entire month, which will run considerably cheaper than buying individual tickets if you travel often, and eliminates the risk of forgetting to buy a ticket (which is costly if caught).

Train rides in Germany range from ridiculously cheap to ludicrously expensive, depending on the trip and when you book it and how flexible you are. I just checked the bahn.de website and could find several options for a round-trip Berlin-Bonn-Berlin for a little over 100 €.

Cooking at home can be a lot cheaper than eating out, however if you are cooking for only one person, then “Mittagstisch” (business lunch) can be quite competitively priced. I don’t much like to cook just for myself, so I was living on that budget and still eating out regularily.

Nightlife and parties depends a lot on where you go. There are both cheap and expensive options. You will want to watch this one as it has the highest chance to get expensive fast if you don’t.

The train tickets are around 25-35€ one way if you order them online, at least 1 month before departure.
Just use the right price portal.
https://ps.bahn.de/preissuche/preissuche/psc_start.post#stay

BUT these budget tickets are dedicated to a specific train connection at a specific time.
If you miss the train, the ticket can NOT be used for a different train, its NOT refundable (unless you use a flexi ticket, which is usually 25% more for the same connection).
Unless it was the fault of the train company (f.e. late arrival).

Also, coffee is around 0,80€-2€ per cup (normal, milk, sugar, not the hipster stuff).

Normal street food should be around 2-4€ if you dont eat right next to some tourist attraction.
Visit some small local restaurants instead of big chains.

Most food stalls provide much better quality and value for money than machdonalds, BK or kfc. Meaning, the sell actual food for around 50% of the price of processed “MC” plastic Stuff.
For around the same price as an overpriced, oversalted fat menu at MCD, you can get the comparatively expensive, but tasty indian street food or stuff from around the world.

Edit:
Sausages in bread are around 2-3€. Also, i ate like that when i visited different cities all over germany, and other parts of europe as a student.
Still eating the same today when traveling (except when i source local ingredients and cook them myself, which i really like).
not sure if other people only associate “expensive, upscale, long waiting time” with the term restaurant. I was reffering to smaller family restaurants and snack shop and stakeaways with seating.
Especially asian and chinese food (except indian) are really affordeable

In general, I would say, this is doable, however in the end it depends also a bit on your definition of “comfortable”. So here are just a few points to consider:

• There are different tickets for tourists (like the Berlin Welcome Card or the City Tour Card) which offer discounted rates (or even free entry) to many museums and other tourist attractions and include public transport. These come at different prices points and validity periods. For regular public transport tickets have a look at the site of the Berliner Verkehrsbetriebe.
• Groceries are pretty affordable in Germany, especially if you buy them at big discounters or supermarkets like Lidl or Aldi. It is no problem to eat well with a budget of 10 € per day if you only cook by yourself. A Döner is usually 3-4 € and basic Asian food starts at around 4 €. Having said that, “small” things like a coffee (3 € or more) or a sandwich (2-4 €) from the bakery here and there might account for a substantial amount of your budget quite quickly.
• Budget wine bought in a supermarket starts at around 3 € per bottle and a 0,5l bottle of beer costs around 50 cents.
• A sim card will cost around 10 Euro, depending on how much (fast) data you need and which provider you choose.
• Round-trip train tickets start at 40-50 Euro, if you choose a saver fare, book them in advance and are flexible with your travel date. You can book them directly at the website of the Deutsche Bahn. (Currently you can only look up fares until the 8th December). Besides that, there are also a lot of flights between Berlin and Cologne-Bonn Airport which start at sometimes less than 20 € for a round-trip ticket. Also: Do you want to stay at Bonn for a couple days? If yes, you have to include the costs for a hotel/hostel in your budget)
• Nightlife is very hard to quantify because we don’t know what type of party you prefer. Generally prices for a beer starts at 3-4 €, longdrinks at 5-6 €, but the prices can also be twice as much (or even more) depending on the location. At clubs there is sometimes also an additional entry fee.

You can buy monthly train ticket for around 70 EUR (2 rings), much cheaper than weekly ticket but it depends on what route you will go on. https://en.wikipedia.org/wiki/Berlin_Ringbahn

Train from Berlin to Bonn can be checked here https://www.bahn.com/en/view/index.shtml, get the ticket early for lower price. At the time I post this, it’s 124 EUR.

A monthly 4G SIM card costs less than 7 EUR on Amazon. You will get 2 GB of data. You can order it yourself and receive it at your friend’s home.

Aside from Turkish and Asian foods, McDonalds and KFC are also reasonable, from 5 to 10 EUR per meal.

I usually have short trip to Hamburg for business and I can say 1000 EUR is more than enough for a month.

Could be a bit short, depending on how much booze and partying you want.

• A 7-day pass for public transport is less than €40. Month passes exist for calendar months or 30-day periods, a bit over €80. I’m assuming that the Bonn trip will be in the middle of the visit?
• The train return ticket is around €130, depending on how early you book.
• Food is possible for €15 or less, especially if you can use your friend’s kitchen and fridge. It makes a difference if you buy prepared sandwiches or bread, butter and the rest.

That leaves €220 for the other points you mention. Museum tickets and nightlife can be expensive. No idea about the SIM card for a month.