Hello All
Sorry to have missed this post, but i think you all managed to get a good consensus.
Anyway, here are some of my thoughts.
The collateral standard IEC 60601-1-1 (aligned with the second edition of IEC 60601-1) was merged with the general standard in the third edition. It´s been revised and some points better clarified. In fact, the original questions are better answered by the third edition than by the old collateral standard. Please see in Annex A - Subclause 3.8 – APPLIED PART -, which has a lot of drawings and rationale to help understanding what is a equipment and what is a system.
1. Would a touch screen panel PC be considered a medical electrical equipment?
As Temujin told you before, the decision on what is an ME Equipment falls on the manufacturer. Under the third edition, there are at least three options when you have a ME equipment and a non-ME equipment. Note that they it doesn´t matter (in the case of non-ME equipment) if the equipment falls or not in the definition of medical electrical equipment).
a - the system is comprised of a ME equipment and a non-ME equipment (the monitor)
b - the system is comprised of two ME equipment (in this case the monitor is considered a ME equipment)
b- there´s no system, the whole is a ME equipment.
Every combination has it´s pros and cons and it´s respective requirements.
Please take a look at the example related to Figure A.7 in the third edition for more explanations.
In any case the basic principle apllies: PATIENTS should only be connected to APPLIED PARTS of ME EQUIPMENT complying with this standard (IEC 60601-1). Other equipment should comply with relevant IEC or ISO standards.
So the touch screen panel has to conply with IEC 60601-1 or with a standard applied to touch screen panels (IEC 60065, maybe?

, or even IEC 60950)
2. If a printer is connected to an ME equipment, what electrical safety standard should it comply with?
The same principles apply, but the printer would have to comply with IEC 60601-1 or IEC 60950 (this is the standard which applies to printers).
3. If a network router is used with an ME equipment, what electrical safety standard should it comply with?
The same principles apply, but the router would have to comply with IEC 60601-1 or IEC 60950 (this is the standard which applies to routers).