I don't trust any thermometer or hygrometer that has not been calibrated. It doesn't matter if it comes with the incubator or you buy them separately. Any of them can have errors.
I use a medical thermometer to calibrate my thermometer. Medical thermometers should be calibrated and accurate...
In a still air (no fan) warm air rises so you get different temperatures at different elevations. A fan can help mix up the air but in a homemade incubator you might still have dead spots.
Those look like quail eggs. Like any others they need to be incubated at a specific temperature (99.5...