Yes, there is a shared pool between EK and Wizard
Yes, you should ignore the original spell slots altogether
In general, I think you are overthinking this. Once you multiclass into multiple classes with spell slots (Warlock is an exception), you ignore the original spell slot tables. Just reference the multiclass spell slots per level table. That will show you how many slots you have.
Spells known are still gained normally. For each level you take you get the spells known as described by that class.
Any of the slots you have can be used for any of the spells you know and have prepared. (Provided they are the correct spell level of course)
Firebolt is a cantrip and cannot be cast using spell slots. (You can cast as many cantrips as you want per day, time allowing.)
That said, a spell you know from your first level of EK can be cast using one of the slots you get from your new 'multiclass' spell slots.
Your hypothetical 6EK/5Wiz could cast the magic missile they learned at first level using their one fourth level spell slot. It would generate 6 darts instead of 3 because of the higher spell slot used.