There is nothing stated in the rules that says Cybernetics take up a utility slot. However, if you look a Cybernetic item in the rules it clearly says it is to be equipped in Utility Slot #1 or #2.
Do you lose a utility slot or not?
If you have a 0 in a Skill and you add +2 cyber skill does it change the number of points you need to upgrade to a 3 Skill or do you syill upgrade as if it were a Skill 0?
You use up a Utility slot while it's being installed, as it has to be equipped there. After installation it's "instanced" on your character and you have full use of both Utility slots.
I got the second question answered on mIRC so I will post the answer for anyone who may be interested.
The +2 is a Skill increase so it counts just like a skill point you receive from gaining a level.
Example: If you have a 0 Skill and you get a cybernetic implant you will have a 2 Skill and any subsequent raising would cost Skill points accordingly. In this case 3 more skill points to raise your skill to a 3.
If you were at Skill level 3 and implanted you would have a skill level of 5 and could not go any higher.
The optimum level for implants would be at Skill level 3 as you are getting the most bang for the buck.
Are the skill increases from cybernetics meant to apply to all aspects of the skill? For instance, is the +2 Strength from the arms supposed to affect max carry weight, HPs, and a/e OR is it meant to only affect carry weight?
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It upgrades the skill, so everything the skill does. Looks like HP may not be updating correctly right away, but should update on level. Kyle is aware of this; not sure if/when he is going to be fixing it.