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yes
The range in 5e is 30 feet. I doubt they changed it but i guess I can't say for sure.
The link Forblaze gave calculates it all for you though, so that's convenient.
Oh, and warlocks are not spell casters in the sense that they don't have the 'spellcasting' feature. Instead they have 'pact magic' and the warlock spellslots are counted separately (though you can use them to cast spells known form other classes and use spellcasting slots to cast warlock spells).
Forblaze is correct. Arcane recovery lets you recover spell slots and spell slots can be sued to cast spells you know regardless of where you know them from (i.e., there is no such thing as a wizard spell slot or a cleric spell slot - the only difference as I mentioned is warlock and that only affects recovery when short resting and total slot determination).
And finally, "nearby ally" doesn't mean anything in mechanics terms. There is no mechanical distinction between nearby or far. Each ability has a specified range and in the case of Projected Ward the range is 30 feet (in tabletop and this is carried over into BG3 but Larian doesn't have the greatest tooltips sometimes...).
No
You will be caster level 2 and able to cast 3 x level 1 spell / day