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I don't own a Switch(so take what I'm about to say with that in mind) but Trading on Let's GO is indeed possible but requires Nintendo's online service to do so if memory serves. You can also import Pokemon from Pokemon GO to your Let's GO game to be caught in the GO park in Fuchsia City(namely you have to "re-catch" the Pokemon you import). Seeing as Eevee version has what the Pikachu version lacks(not to mention the 4 traditional Trade Evolutions in Machamp, Alakazam, Gengar and Golem), it would be extremely shortsighted to remove Trading from the Pokemon games.
You can; you just need to pay for Nintendo's Online subscription.
Then, step by step:
1) Press X and select "Communicate"
2) Select "Play with Others"
3) Select "Nearby player" if you want to trade or battle locally, meaning if they are in the same room as you.
4) Select "Trade" and you'll have a screen pop up to select a code. You'll have 10 Pokémon to choose from to create a three-Pokémon code, this is to make sure you connect with your friend locally.