How to transition from using linear to switching voltage regulators?
Answers to 1 and 2 should come mostly from the datasheet of whatever switching power supply chip you plan to use.  First you have to make sure the chip is intended for your input voltage, output voltage, and maximum current.  After that you need to follow the directions, carefully.

These kinds of chips are designed assuming a certain range of parts external to them.  The datasheet will tell you what is acceptable and it may even give you some guidance what values to use over a range of parameters.  For example, the datasheet might recommend a larger inductor for the upper half of the input voltage range.  However, you'll probably pick a chip because it's max characteristics exceed your requirements by some reasonable margin.  In that case, you follow the recommendations for the max case, since that's effectively what you will be using.  Some datasheets assume this and only give you one set of recommended values.  Just follow them.

As for question 3, yes, switching power supplies can cause more EMI.  The main trick is to keep all the local loop currents localized to the power supply sub-circuit, and to keep these loops physically small.  This means starting with a good layout, then carefully routing the key nets.  Make a separate local ground net for the switcher, then tie that to the main ground in only one place, probably right at the ground side of the output capacitor.  This keeps the loop current thru the diode, inductor, and output cap localized and off your main ground plane.  Only the net delivered current should flow thru the power and ground feed points from the power supply sub-section.