Where was the computer skill split up into operation, programming and hacking

Those numbers are your overall modifier for that skill or saving throw. They include your proficiency bonus if you are proficient in them, otherwise they are just your ability modifier for that skill or saving throw. They're pre-calculated and listed on the sheet for convenience during the game so that you don't have to add up all your modifiers and Proficiency bonus every time that roll is made.

So if your example Cleric is proficient in Wisdom saving throws and has a Wisdom score of 15, their Wisdom saving throw modifier = proficiency bonus (+2) + Wisdom modifier (+2) = +4, which is the number that will be listed under Wisdom saving throws.

On the other hand, your Cleric probably doesn't have proficiency with Dexterity saving throws, and let's say their Dexterity score is 8. Their Dexterity saving throw modifier = no proficiency bonus (+0) + Dexterity modifier (-1) = -1.

There are other factors that can affect this calculation, such as the Rogue's Expertise feature, but this is the basic calculation that will be used in the vast majority of cases.

The very simple answer is that you are only trained in a skill if you have at least one skill point in it.

You can read and write (and speak and listen) in any language that you know, the linguistics skill would be used if the character was trying to create a forgery (which is much more difficult that simply writing it yourself, as it needs to be presented in a certain style, have the right handwriting and seals, etc). If they just want to copy a document and not pass it off as an official copy, then they should be able to do so without the use of the linguistic skill.

Bonus languages from high intelligence at creation are just that, bonuses. The fact that you also get extra languages from putting points in the skill does not mean that they are the same thing.