This is one of my favorite systems and I've learned a lot playing it, so I apologize in advance for what will probably be a wall of text. You can TL;DR the bold bits.

Black dice are like salt, sprinkle some on everything - Black dice are a great way to add adversity from the world (poor visibility? suspicious guards? time crunch?) and a good way to use generated threat (distracted, damaged gear). Also, many PC talents allow them to peel black dice off of skills they specialize in - and players really enjoy telling the GM they don't have to roll the bad dice.

Blue dice are like pepper, add a little to most things - They're a great way to reward players who have a clever approach, tie in to character backstory (my former-pirate probably knows who to fence stuff to around here), good roleplaying, or good preparation.

Facing a player with something they're good at is cool, facing a player against something they're bad at is interesting - You want a healthy mix of both. A gunslinger PC wants to take out hordes of mooks and absolutely should get the chance to let loose now and then. But if the party disguises themselves as maintenance personal as part of a heist, that same low-int gunslinger should be flagged down by one of the staff and asked to fix a broken grav-lift. It puts the PC in a tense situation where they have to think (I can shoot my way out, but that blows our cover. I can try to fix it but raise suspicion if I fail. Can I create a distraction? Can I talk my way out?). Making scenarios like this happen isn't too hard because...

Splitting the party is a great idea - As others here have said, combat balance is basically non-existent in this game, so a split party isn't a death sentence in combat (and even losing combat isn't usually lethal). Also, escaping from combat is much easier in this system than others (Hop on a speeder, hack a door closed, or just use a destiny point and shoot the door controls). Comms exist to keep the party in contact and allow them to coordinate/affect each other. (One character can make a distraction to allow the hacker to slip into a building - the hacker can then help the thief get past security, etc.) A combination of multiple objectives and time-pressure is a great way to get the players to split up. (And the Obligation system is great at creating secondary objectives for this purpose)

There's plenty of time to get things done in combat - Unlike DND, combat doesn't put a dead stop to everything else that's going on. The rules say that one full round of combat in this system is "one to several minutes". If combat breaks out, party members can still use skills, hack things, get to places, have conversations (probably away from the firefight). Very often in EotE, my players found themselves in a "fighting retreat" after tripping an alarm and needing to finish the objective or escape, it keeps tension up and you can use minion groups as reinforcements for added time pressure.