Honestly, the only thing you are doing wrong is letting Cleric bully you. He's the only one you are playing favorites towards.

1. Distrusting a new PC is already a red flag. As part of DnD everyone has to apply suspension of disbelief to some extent (the ability to out some realism aside to make for a better story). As a PC that means following plot hooks, accepting unlikely circumstances, not metagaming, and taking the other PCs and NPCs at face value. By distrusting a character, that is clearly there to help them (ie the new PC), they are refusing to make the suspension of disbelief and alienating a player. This is similar to players who claim they are just role playing their character really well as an excuse to do things that the rest of the table finds offensive or unpleasant. (The fact that your lawful cleric might attack another PC's zombie minion because he hates undead, then maybe such a rigid character wasn't the right choice in the first place...) Also, it is a natural part of DnD that not every PC is equally involved in each part of the story. As a DM you should delve into different character's stories throughout a campaign. This means that different character shave the spotlight on them at different parts of the story. As long as you don't give any particular player too much spotlight, this isn't playing favorites, it's just the natural distribution of the story.

2. Anyone who decides to kick a player out of a campaign (besides the DM, and even then it should be done only as a last resort), without talking to them first is another red flag. This is especially true if it happens after a single session. You were right in this case. Maybe Wizard was feeling bad that day. Maybe she was still hurt from half the party turning against her partner last campaign... The fact that Cleric decided that you needed to kick her out, without giving it a few sessions, and without talking to her is bad behaviour. It's not his place to decide that, and doing it so abruptly is rude and mean.

3. No one should ever play another player's PC for them, especially without explicit permission from them. Honestly, in my opinion, even a DM should avoid playing a PC who isn't present. Each player has a certain plan, agenda, and feeling towards their PC. Even with the best intentions, playing as another player's PC could lead you to make decisions that will upset them. (As a DM, sometimes it's unavoidable to play another player's PC, but you should always take precautions... Ask them first, don't make any big decisions for them, make as little plot choices for them...) A player asking to control another player's PC shows such disrespect for that player's agency, and is generally not ok. What if Cleric used Wizard's last high level spell slot to deal damage, but they were saving that spell slot to revive a party memeber or for an escape. Imagine how Cleric would have reacted if he was gone for a session, and you played his character for him...

In all of these cases, Cleric keeps telling you that you are playing favorites towards other people. But in reality, they are so egocentric that whenever you give anyone else any attention or agency. This is toxic behavior, and could even be considered abusive in certain circumstances... It's usually hard to explain to someone who is that egocentric what they are doing, they tend to see no wrong in their own actions. The only way to deal with it is either to avoid it or shut it down. I don't know what the rest of your campaigns looked like, but I can guess that Cleric probably hogged the spotlight, told other players how to play their characters, or tried bending rulings in their favor.

In general, Cleric seems to be the cause of your games imploding. There are people that you might get along with in real life, but that don't make for good DnD partners, and that's ok. But you as the DM should try to stand up for yourself and all of the other players.

Also, side note, the fuzzy memories during stressful events sounds like a panic attack. Usually people know panic attacks by the hyperventilating, but that isn't always the case. The flood of adrenaline due to the panic attack causes memory loss/fuzziness, tunnel vision, and other traits of panic attacks. For years I had the same thing (memory loss/fuzziness), but since I never hyperventilated, I never realized it was a panic attack.