Upgrading a Shimano dinosaur?

My daughter has a ten year old MTB with Shimano 18 speed gearing. We like the frame and want to keep it, but upgrade the gearing.
So I've bought a Shimano "Megarange" screw-on freewheel. This has a biggest sprocket of 34T. The existing biggest sprocket is 28 teeth.
Will I need to replace the existing derailiur? Will any long derailiur do, SRAM, or Shimano?
Will any 7 speed shifter be a suitable replacement for the existing 6 speed one?
So I've bought a Shimano "Megarange" screw-on freewheel. This has a biggest sprocket of 34T. The existing biggest sprocket is 28 teeth.
Will I need to replace the existing derailiur? Will any long derailiur do, SRAM, or Shimano?
Will any 7 speed shifter be a suitable replacement for the existing 6 speed one?
my baby elephant would rather walk than be a Campag snob
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you will need a new chain whatever.
Parktools :?:SheldonBrown