While much has been said about the price and legal aspects in other posts, I am trying to give a bit of a cultural perspective in this answer (at least as far as I perceive it, as a native German who regularly likes to go to not-too-expensive (meals between 10 and 15€) restaurants with varying groups of people).
In German restaurant culture, drinks are considered about as important as food.
Typically, a short while after guests have sat down at the table and received the menus, a waiter will ask them what they would like to drink. Guests are then given some more time to study the food part of the menu before the drinks are served and the waiter will ask for food orders.
When the waiter arrives to accept drink orders, it is kind of expected that everyone will order a beverage to consume along with their food. It is certainly not unheard of that someone will only order some food, but it is slightly unusual (as in, a few people order only food out of a personal niche habit, but most will order something to drink).
Accordingly, most German menus I have encountered have an extensive drinks section with various alcoholic, non-alcoholic, hot, and cold beverages. Choosing and trying an interesting-sounding beverage from the drinks list can be given just as much attention as choosing and trying an interesting-sounding dish from the main courses.
This leads me to the following concrete answers to your questions:
It is said that in Germany asking for tap water in a restaurant is rude and looks stingy - examples in here and here.
But I don't like to purchase water there as buying it in a restaurant would likely be too expensive
Well, don't order water. There's a plethora of dishes to choose from, so you wouldn't order something as bland like a buttered slice of bread. Likewise, there's a plethora of beverages to choose from, so you wouldn't order something as bland as a glass of water.
(Caveat: Those Germans who do order water do, in my experience, connect some sense of exclusivity with the presumably particularly high-quality bottled water they will get served.)
So I wonder if it is rude to buy it somewhere like a convenience store or supermarket in advance and bring it to a restaurant.
Even without the probable violation of house rules1: Yes, it is just as rude as buying your food in a convenience store or supermarket and bringing it to the restaurant.
Or is there anything others you can drink in cheaper price while eating?
As I mentioned above, the set of available drinks is not a secret. That is, you don't have to rely on "insider knowledge" to know what you can order besides water. Along with the menu for choosing something to eat, you will get a list of available beverages (either as a part of the regular menu, or as a separate booklet) that will normally list both the price and the volume of liquid you will get. Like this, you can choose something that best meets your requirements for liquid intake and monetary expenses.
1: Note that those are not necessarily very easily visible in Germany. Maybe it is legally required, and maybe they are indeed posted somewhere, but it is usually understood as common sense that you cannot consume anything bought outside in a restaurant in Germany (except due to dietary restrictions, as explained in another answer). However, in some highly-frequented tourism spots in Austria, I have actually seen some restaurants that had very visible warnings signs threatening to charge a fine if someone is spotted consuming food bought elsewhere.