Each set is unique and works best within its own set, however, there are many cards that work very well with other cards from other sets. As a general rule a set works best within itself, the affiliations in a set work best within its universe (Marvel, DC, Dungeons and Dragons, etc.), and an individual card from a set has the best potential to find synergy outside its set or universe.
Yes. All sets are made to work together. You are free to use Batman, Spider-man, and Red Dragon on the same team, for example. Some sets, however, have used different terminology or symbols that correlate that you will want to make sure you know:
From the rulebook:
“While you can use heroes and villains together, or characters from different teams, you can’t use two cards with the same name (even if they have different subtitles)”
Also, even though some character dice may have the same image and stats between different sets, it is generally not acceptable to use dice that do not match the card/set in a tournament setting. This is determined by comparing the die to the images at the bottom of the card to make sure all colors, symbols, and stats match. If you are playing casually and your opponent is comfortable with you using a mismatched die (generally a different color with the same stats) you may use a substitute die.