If a player character dies, I try to make sure it is meaningful in the moment. They get their last words or their dramatic fall to the ground, and depending on the character, they might receive some vision based on their god or whatever.
Moving on past it, usually the player whose character died chills for the moment. Assuming the party has no way of reviving them at the moment, there is usually an in-game discussion on if reviving them is even an option. Out of game we might also talk briefly about if the player wants a new character, or if they want to be revived.
Assuming the revival can’t happen that session, I’ll have the player make a new character and I’ll make sure they are introduced within the first hour of the next session. I hate, hate, hate nothing more as a player than having a session where I literally sit out waiting to be introduced (happened to me twice) for hours IRL.
The only really hard part is if that character had important backstory stuff tied to the big main stuff going on. Just need to be creative, find a way that the plot can still move forward. Or, perhaps it changes the direction the campaign goes - never be afraid to toss your plans out the window.
As for balancing things, it’s truly a trick. I would start softer and ramp it up. The most important piece is learning what your party is currently capable of, and how much punishment they can take before they would break. But never forget three things.
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Action economy is king. The more actions one side can take, the sooner they can win. Remember that if one player falls, it not only means that player is down, it means the rest of the party must now fight even harder AND use action economy to perhaps heal/save them or at least protect them from further harm.
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The dice can truly be a blessing or a bane (hah). You can handcraft a “perfectly balanced” encounter but the dice will force a different story. Even just the initiative roll can decide combat: once I was a player, around lvl 10 or 12 or so. We got ambushed at night by a fire giant. Rolled initiative, fire giant went last, with me just before. Everyone hammered into it, and then I finished it off with Disintegrate. It didn’t even get a chance to move lol. On the flip side, I’ve seen easy encounters become practically deadly because of bad dice rolls.
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(Super illegal tip, keep this on the hush) You can adjust encounters on the fly. You can change the monsters HP. You can add more monsters in or take them away. You can fudge a roll and say the bugbear trips. You can give the TRex the ability to teleport. You should not get in the habit of doing this - if you are adjusting on the fly, it implies that you are controlling the encounter to go how you want it to go, which means removing player agency. Bad. BUT if you’re a new DM and you accidentally make an encounter WAY TOO easy/hard, this is your secret weapon.
Key tip with this: once info is known, don’t change it, unless there’s a reason. So if your players attack a Wyvern and a 15 hits, then a 15 should be a hit every time, unless maybe thematically that hit ruined/removed its scales and so you lower the AC.
Sorry that’s a lot lol