No (or yes, depending on how you define a single trade).
The person whose turn it is can trade. Each trade is with that person and one other person.
If you can accomplish what you need in a series of trades, you're welcome to try. But any promise of future trade is non-binding: your later trading partner may legally decline the trade when it comes time.
Absolutely. From the website, Exploding Kittens is a:
Party game for 2-5 players (up to 9 players with 2 decks)
I often combine the Original and NSFW versions, to play with more than 4 players. You just have to make sure that there is always exactly 1 Exploding Kitten card less than the number of players.
The Catan Compact now has an official variant for two players, you can read the rules here. It only needs an additional set of trade cards, aside from the base game components, but you can easily make these up by yourself if you have the non-compact version [e.g. use a standard set of cards].
We play to 50 with two players or 40 with three players. Complete different strategy to win. We have also played with six of each color for two players, or only two golds. You can also only lay out three cards of each, instead of four, or put down no royals.