Power cable thickness q:

What kind of cable should I use to connect seven 50 W light. The cable draw power from a 10A supply.
One thing I do not understand is that I have to use pretty thick wire but table lamps have thin cables. What's the story here?
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You have 350 watts. If you are operating a 120 volts, you've got less than 3 amps. The smallest recognized building conductor size is #14, which is good for 15 amps

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The size of the wire will depend on how far your lights are from the power source.
In simple terms there are low voltage/high current circuits and high voltage/low current circuits. The larger the current , the bigger the wire will need to be to carry the same ammount of power. If the wire is not big enough or too long for the size , the voltage will drop in the wire and the light will not be as bright.
A 50 watt light operating on 120 volts will take about .4 amps and you can run small wire a long distance. The same light operating on 12 volts will about 4 amps. That is a 10 times differance so the wire will need to be much larger.
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If this is a typical house wiring job, say to install some ceiling lights in a dining room, then 14 gauge Romex is what would typically be used. But it can also depend on the location and other details of the install. Since this circuit is only 10amp, it must be fairly old wiring.
The cable for 7 lights has to be a heavier gauge than the wire for one table lamp because it must support the load of 7 lights, not just one.
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Re Power cable thickness q::

Use #14
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