I can understand why you wouldn't want to use the input field, as this increases the effort the user needs to use the filter. But in cases like yours where you have described, you don't have a concrete range, the input field is the best solution.
The other solution you can use is to have ranges for the most common ones and also have the current input field ...
The UX answer would be to provide the best experience for your customers.
If full-width is your solution then you will need to create and implement designs for multiple break points.
To answer your question directly. No.
980px is useful as approximation for a desktop users. It works on designs for 1024 and above. Example: a design with side margins.
It looks like you're trying to build a style guide. If so, then you really need to work closely with your UI designer to define/refine the colour palette and its usage.
Style guides protect you from team, supplier or product changes. If you get a new requirement from the product owner, the style guide should tell you how it will look. If you have to scale ...
Devices in the wild are too diverse for a single size to work well for everything.
Design for the widest monitor you'd expect, likely around 4096.
Create differently sized variants for smaller monitors. Could be via rescaling or cropping or other means.
Trying to use a pixel width for a standard size has been a losing battle for years and no web developer or designer should have that as a goal. You do not know, and cannot reliably determine, the size of anyone's display size. So don't do that.
The best response I've ever read about this question is, start with the smallest possible display width--which is ...
IMHO, I don't think 980 is a good rule of thumb for anything fullwidth on desktop or tablet anymore, especially because of "retina" displays. If I had to choose one resolution to rule them all, I'd probably go 1440 or 1920, but you're still going to be shooting in the dark there and adversely affecting users with poor connections.
Some of this depends on ...
I don't see new screen creation as a significant problem because the stack of screens is limited by user behavior, which is finite, unless there's potential data inconsistency. Some options to consider:
Change link behavior so existing screens are searched for previous instances to call forward before new screens are created.
Change "back" behavior so that ...
Depends how much time / effort you want to invest. You could;
create paper prototypes, different screens, and ask users to simulate clicks with finger, then change paper
Create low fidelity prototype in Sketch / Figma, do same thing
Create high fidelity clickable prototypes in Sketch / Figma, and serve them on real device for user testing
Case like this I really suggest program called "Figma", its really simple and fast to create good looking mockups and you can also do the interaction with it. Figma provides also mirror tool for phones so you can actually test it with mobile phone easily.
edit* You can use Figma on browser or desktop app, you can also use it out totally free!
As the price range is just an estimate, entering a min and a max value can be replaced by a single price estimate and a margin of error as a percentage.
The price estimate would be a single value slider (exponential as in my other answer) and a radio button list with +/- 5%, +/- 10%, +/- 20%.
You can display the resulting range as a confirmation.
If you know a minimum and a maximum value, an exponential scale is what you need:
When the price range is very wide, it is difficult to enter the desired value using a slider. We've all experienced how annoying it is to try to find the exact pixel position of a slider to get the desired value.
Additionally with a linear scale, each slider step has the same ...
If I understood it right, I think the best approach is to have the text field on the left, always the mobile attention and actions are taken from the top left to bottom right. unless you don't have grids so the text field is better to occupy the whole width to be centered which is more usable and more comfort for the user.
Here I attached a screen to show ...