An smg is a sidearm weapon so no it would not effect both weapons...light skill effects light weapons.

Which ones are the light weapons?

If you read the item description, either in the market or in your 'Edit Dropsuit' fitting screen and hit triangle when the wepon is hilighted, you'll see the weapon type.

The only way to have skill bonuses apply to both slots would be to have two sidearms, say a pistol and a smg. This might work out ok, pistol would be your long-range weapon and the smg your short range/fallback weapon. Would save you on the skillpoints until you spec into AR, which is a light weapon.

I have another question. I upgraded this skill "Sub machine gun operation (2x)" to level 4. From the description of the skill it should increase my smg damage by +5%. Will this change the damage on every smg in every dropsuit I have or do I equip this to a specific smg?

Yes, the bonus is applied to the character, not the weapon. So you do not need to re-equip, you already get the bonus by virtue of increasing the skill.

Can anyone explain what is the difference between Electronics skill and engineering skill?

thanks

Electronics is about CPU/Shield mods.
Engineering is about PG/Armour mods.

Not 100%, there are other things besides shield/armour mods that are covered by each, but that's a basic idea. You could just look at the skills and their relevant sub-skills in the character sheet for that answer though.

not 100% accurate

electronics = CPU / equipment like scanners/ecm
engineering = PG/shields
mechanic = armour/repair