Transformers with 16 Volt AC voltage or DC voltage are recommendable. Older transformers are not recommended, due to the danger that the LEDs break by overvoltage. In addition it is to be noted that the Transformer is switched off when it is not used.
It could be possible, but really not recommendable. The batteries would be used up within some hours. By long-term usage the LEDs simply use too much energy. Therefore the use of batteries is extremely expensive.
When attaching the object it is to be noted that the cables are not allowed to be pulled. Touching the LED could possibly cause a defect. You should be aware that you should make a large hole, so that at least one of the resistor fits through the hole loosely. If the resistor in the hole wedges, do not pull the resistor. Take it out carefully again and drill a larger hole. Resistor should be fastened under the plate in a way that no short-circuit can develop. In addition it is to be noted that resistor should have enough air supply, because they get hot after several hours. However there is no danger of burning yourself.
The resistor must be attached to the mass (brown) and may not be coupled to current (yellow). The overvoltage protection (protection diode) is attached to the current (yellow).
In order to be able to dim a LED correctly, a second resistor should be fastened to the first resistance. They must be switched into row. It is also possible to attach several resistor at a further resistor, thus the LEDs are more strongly dimed. If the total Ohm number of the resistor is too high, the LED remains dark.