Can I use 16mm or 10mm DC cable for AC home appliances?
If you do not know what cross-section or gauge of wire is appropriate for installation in a home or business, you should not be installing it, period.

There isn't a single "correct" type of wire to install, instead there are many factors which relate to:


Local laws and building codes
Amount of current drawn by the appliance(s)
Number and type of outlets and total expected load on the circuit
Type of breaker required (arc-fault, GFCI, etc.) (see #1)
Inspection and testing (see #1, again)




You should contact an electrician to add or modify your residential wiring. If you insist on a do-it-yourself (DIY) approach, you should research your local electrical code and look for information on the above points. In order for that effort to be productive, you should first make sure you understand the following fundamentals:


voltage, current, and power
alternating vs direct current, polarity, neutral vs protective Earth/ground
wire cross-section/gauge; current capacity; resistance and voltage drop over distance; temperature derating; etc.
series and parallel circuits
electrical safety, circuit breakers/fuses, proper use of voltmeters (multimeter), etc.




As you can see there's a lot of basics that must be taken into account in order to answer your question:


How many amperes do your appliances draw? Do they require the same voltage? What sort of insulation is required based on fire code and voltage rating? (Your local laws dictate this.)
There's no such thing as a "DC cable."
What does "16mm" mean? If you mean 16 mm² (roughly equivalent to 5 AWG), that's a massive wire diameter for casual residential use, even for major appliances. (Some countries refer to wire diameter as 'cross sectional area', usually in square millimeters (mm²). Others use wire gauge, also known as American Wire Gauge (AWG). The superscript '2' is important.)
I presume you don't mean a wire length of 16mm, as that's impractically short for any appliance purpose.
Most wiring is sold as having a number of conductors, not cores; and for most residential and commercial wiring, three or more conductors are used (e.g. line, neutral, and protective earth/ground). Therefore, two is likely not appropriate... Unless you're talking about a replacement cord for a small appliance or fan, where such devices often have only a two-conductor power cord. This, however, would not be considered "installing wiring in your home". Instead it would be more of an "appliance repair" or a "replacement of power cord." If so, this is a more reasonable DIY project, which your local hardware store can assist with.
I am suspicious you may be meaning a two-conductor 16 gauge (not mm) cable to replace, for example, the power cord on a fan. If so, you should be able to inspect the damaged power cord and replace it with the same (or thicker) gauge. Again, your hardware store can assist. They also will have replacement plugs in case you only need to replace the plug and not the entire cable. If you need to open the appliance/device to attach the new cord, you may encounter other problems. For example, if you are not familiar with soldering or crimp terminals on wires, etc.