I would like to know an estimate about costs and time needed to do this kind of existingPC games ports.

How long will it take your team to do it? Multiply the time by your man-month cost, thenadd your profit percentage need. It's not difficult math (assuming you can make a reason-able time estimate).

Try to figure out an estimate about how many peoples you need the time and the cost to finish the project and have Half-Life 1 full version apk working on android.
....
Than try to estimate the cost of the work developing Xash3D as it is. Hiring engine programmer or whatever you need and the time to do that.

At a rough guess -- one engine programmer for a year, full time.
The median salary for an engine programmer in the USA is $130k. There's other parts of the world though where you might find a talented engine programmer who is happy to work for USD$50k...

Maybe you can also find one who will work for free now, but they will own half of the business with you? But for that, you would have to be putting in an equal amount of work as they are.

If a client came to me asking for an exact price for this, I would need to spend a few weeks investigating the source code so that I could start planning the project and estimating the tasks involved... That initial investigation alone would probably cost ~$2000-$8000.

Not so easy since i have no developing skill. I would like to find and pay a team able to do that...

Then you need to get the contract with the other company as well. THEY will need to estimate the work.

Ok but you think there are available games might be easier to port on mobile than others?

Yes. There will always be games that are more easy to port than what you described.

In the absolute best scenario, it would be a simple game, it will have already been implemented on the PC for touch screens, it will use an engine that has automatic support for the target platform (such as Unity, or Unreal, or GameMaker:Studio or something similar), the game will have minimal resource needs that fit easily on your target devices. If the stars align in such a game, all that is required is picking the target system, building, and playing.

I say that cause would be better to choose between something with less requirements. Just asking you don't know if this possibility even exist.But pheraps there are games using a certain architecture that would be more compatible with other platforms from the beginning trying to guess

Every game will be different. Two games that appear very similar may have enormous differences.

Already mentioned above is the game engine. If one is a complex game written with a complex code base relying heavily on Windows core API calls and Direct3D, and makes strong assumptions about the Windows OS environment, and if another is a complex game written in a game engine that abstracts all the OS-specific components, the second will be easier to port.

Even if the game is using a platform-friendly engine, the game may be coded in a way that relies heavily on a platform-specific resource. For example, Titanfall was primarily written for game consoles that have dedicated audio hardware. On those platforms there was almost no effort to use the audio processor. Their initial PC release made an assumption that an entire CPU core could be dedicated to the same audio processing. When that didn't work, they ended up patching the game to include 36 gigabytes of uncompressed audio because the PC did not have the proper hardware resources.

Even if the game is using a platform-friendly engine and not using hardware-specific resources, the resources on a mobile device are far different capacity. Processors are slower and don't have the incredibly fast, but power hungry, features of the x86 family like an out-of-order CPU core and enormous memory caches. The data bus is smaller and slower. Graphics chipsets are far less power. A game on a PC or game console might render a complex scene with around 5000 draw calls or so, but on a consumer mobile device you may struggle to get more than 50 draw calls. Data storage is different, memory is different, audio is different, graphics are different, many systems have different capacities and performance characteristics.

Even if you are using a platform-friendly engine, and the game doesn't rely on platform-specific resources, and the game isn't relying on platform-specific resources, and it won't be limited by hardware-specific performance characteristics, it can be limited by other factors. The user experience may be different, or the way the device is held, or the estimated playing time, or network connectivity, or screen aspect ratios, or mechanics relying on hovering over elements, or differences between click or typing or touch, or two-handed versus one-handed experiences, or tons of other factors.

The game itself needs to be considered. The difficulty of the mechanics to port, the difficulty of the story system to port, the difficulty of the gameplay systems to port, etc. Some may need no modification, some may need to be rewritten.

Tools need to be considered. Build chains need to be considered. Data formats and intermediate files need to be considered.

There is no way to know without looking deeply into the systems and the code and evaluating it. One game may be nothing, requiring only a settings change.. Another game may be $50,000. Another may be $750K. Another game may be $3M. Another game may be $50M, requiring nearly a full rewrite of a major game.

This is not a good area for guesswork.

I have worked with several companies who purchased full published game engines and attempted to revive them, to port them, or to bring them up to modern standards. Some of them were a pleasure to work with, very quick and easy. Others we evaluated the costs, and after the company learned from one or more contractor that the cost will be an 8-digit cost, they realized their mistake and cut their losses.

If you don't have experience with porting from the source system and to the target system, and if you don't have firsthand knowledge of the systems involved, you are not the right person to make the estimate. If you are contracting that work out you need to have the contractors evaluate the work and make their bids from it.