How TS Doctor decides where exactly to cut?

[Indirect]

You have described earlier:

The TS-Doctor can cut in at I-frames and cut out at I-frame or P-frame.

Is this correct only when setting "Consider I/P-Frames for cutting" is checked?
To clear out for not english-native-speaker: "cut in" means where wanted area begins, "cut out" - where ends, is that correct?

Could you please describe, is TS Doctor searching back or forward (in relation to cut in mark I've placed) while looking for I-frame to cut at?
Does it mean, that cut out will be exactly at the place I've placed my mark?
What does exactly setting "Prefer cutting before cut out point" mean?

How cutting would work if the "Consider I/P-Frames for cutting" is unchecked?

Thanks alot!

[Cypheros]

Is this correct only when setting "Consider I/P-Frames for cutting" is checked?

Yes

To clear out for not english-native-speaker: "cut in" means where wanted area begins, "cut out" - where ends, is that correct?

Yes

Could you please describe, is TS Doctor searching back or forward (in relation to cut in mark I've placed) while looking for I-frame to cut at?

Nearest, can be before or behind the desired point.

Does it mean, that cut out will be exactly at the place I've placed my mark?

No, the TS-Doctor is not frame accurate because this would need reencoding of the cutting area.

What does exactly setting "Prefer cutting before cut out point" mean?

After the desired frame for cutting there is in most cases a commercial break or something like that. If it's important for you to have no advertisement frames in the final file you can use this option to let the TS-Doctor only search before the cut out and not behind.

How cutting would work if the "Consider I/P-Frames for cutting" is unchecked?

The TS-Doctor is ignoring the frame types (I/P/B) then. The PES start condition following the cutting point will trigger the cutting. Most likly you will get more picture errors at the cutting area because disabling this option will lead to incomplete pictures.