Removing the dish washer should be straight forward (turn off the power and the water first). I speak from experience.
The water lines may have valves that can be turned off just like a washer dryer. So just strap them out of the way. Plugs can be obtained from any hardware outlet.
The cabinet will be the most difficult depending on your taste, skills and tools available. You could do drawers?
How difficult? Not very if you are handy, could be tricky if you truly are not handy. Most people taking their time and asking questions and seeking help can do this stuff.
A router and some knowledge of how to use one is a very important tool for this kind of work. Particularly if you want to match the existing cabinetry.
Maybe a local cabinet shop would make you a slide in unit (just like the DW'r) with drawers or doors from your measurements.
Then you just pop it in and screw it in place. You may not like the price but it is worth asking. They may also give you some hints.
Lowe's and Home Depot sell pre-made cabinets for bathrooms/kitchens. Maybe one would be just the right size and could be adapted to your use.
I do all my own stunts
03 Dolphin LX 6355, Workhorse W22, 8.1 vortec, 04 CR-V, Blue Ox, Brake Pro----Norm, Barb and
Doc(He's a PhD)