Wall switches/simple dimmers deal with one function only, the starting/stopping of nominal 120v ac electricity going to the fixture which contains the load. Only the load should have a neutral (white) line leaving it plus the switchable line from the switch entering it. So your old switch should have two wires connecting to it, one bringing in 120v power (black?) to the switch and the other (hopefully not white) when switch is "ON" sending power to the fixture. The dimmer you purchase will contain installation instructions to thoroughly cover all this without doubt. Here is a link that might be useful: Install dimmer

I have an aversion to ill-lit kitchens, so I'd look at an LED Tube Puff style ceiling fixture and a pendant or two over the peninsula. Pendant Lights In the living room, how about something like [THIS[(https://www.houzz.com/products/wooden-3-light-chandelier-prvw-vr~81079779)? JM$.02W

I have a similar situation where I have light fixture in kitchen, dining area and living space all within 20 feet of each other. I am terrible at having fixtures 'blend' - especially 3 of them, so I opted for a wood fan. Easy way out but at least it kind of works and looks more finished. https://www.houzz.com/products/minka-aire-light-wave-fan-distressed-koa-prvw-vr~92222205?lid=71144359  

Yes it can be done, if you are not a wires person I suggest getting whoever is hanging your new light to swap out the switch for you.