A charger was included, USB-C, Max 65W, Model ADLX65YLC3A, Input 100-240V 1.8A 50-60Hz, Output 20V 3.25A/15V 3A/9V 2A/ 5V 2A. The transfomator is approx. 3x5x12cm. As a rule, other USB-C chargers also work.
I use my LG monitor via HDMI connection. This simply requires a USB-C to HDMI adapter. I have a Satechi adapter, also from Digitec. The MOnitor also has other connections, but I have never tested them.
Yes. According to the manufacturer's number, the information is correct: http://psref.lenovo.com/Detail/Lenovo_Tablets_and_Convertibles/Yoga_730_13_Intel?M=81JR002QMZ
I can't say much about the first part...
UHD is not 100% the same as 4k. 4k is 4 times the resolution of the cinema format 2k (2'048 x 1'080) which results in a final resolution of 4'096 x 2'160.
The normal screen ratio of consumer devices with FullHD deviates slightly from the 2k resolution of the cinema projector 1'920 x 1'080. If we now double the lines here, we get a resolution of 3'840 x 2'160.
In other words, the difference between 4k and UHD is that the 'orignal' 4k applies to the cinema resolution and consumer devices have a UHD resolution. In marketing terms, it is now used as a synonym.
The performance is very good and the CPU is fast. For Office & Internet, the battery lasts about 8 hours. However, a development environment or the Adobe Suite reduces the time to about 4 hours. With the Windows performance settings, you can save the battery at the expense of performance. When the CPU is fully loaded, the fan is really loud and annoying. But that has only rarely been the case with me. All in all, I think it's a great device. I find the pen with OneNote particularly powerful. It works great.