In the book, it says that Move By Wire gives +1 Dodge, +2 Reaction and +1 Initiative pass per level.

Does it mean:

Level 1: +1 Dodge, +2 Reaction, 2 total Initiative pass, Skillwire Lvl. 2
Level 1: +2 Dodge, +4 Reaction, 3 total Initiative pass, Skillwire Lvl. 4
Level 1: +3 Dodge, +6 Reaction, 4 total Initiative pass, Skillwire Lvl. 6

or

Level 1: +1 Dodge, +2 Reaction, 2 total Initiative pass, Skillwire Lvl. 2
Level 1: +1 Dodge, +2 Reaction, 3 total Initiative pass, Skillwire Lvl. 4
Level 1: +1 Dodge, +2 Reaction, 4 total Initiative pass, Skillwire Lvl. 6

?

Also, a character that have a dermal sheath with ruthenium polymer and chameleon option, does he have to be NAKED to benefit of the effects?!? I mean... what about his gun? What about his armor?

The first list of benefits is correct.

For the ruthenium treated dermal sheath, you have to be naked for it to work, and any weapon larger than a pistol has to also be coated, along with your gear or the benefit is halved.

Per level get the benefits added each level, so I'd go with the former block of stats.
In my home games I've insisted that yes a character has to be at least 80 percent exposed to get benefits of Polymer on the skin.

Use the Ruthenium-Polymere covered Armor-Suit instead.
Save Essence and you can get rid of it/have it repaired.

Do ruthenium panties and bras exists?

Yes.