IKEA Loviken Faucet disassembly assistance requested
When the interior phillips is loosened,


You should remove it, not just loosen it.

Then the handle should lift off vertically.

This should allow you to remove the cover/washer part

Then you should be able to see the hexagonal top of the valve assembly
and remove it with the corresponding sized spanner wrench (or adjustable nut-rounder)


  My kitchen faucet drips a bit


I'd investigate if the valve unit can be tightened and whether everything is seating correctly / whether there is trapped debris or damage. There might be a rubber/plastic washer you can replace.


  I'm also unsure if part 118211 is easily replaced here in the US


It is easily replaced in the US, it might not be easily obtained in the US :-)

I'd 


Ask IKEA about obtaining replacement part 118211.
Take part 118211 to the local hardware store / DIY-shed and show it to the oldest person there.
Send money to Sweden.