If you go down the WD40 route, don't spray it on. Use a pin to touch a drop into the joints that are sticking. You only need a tiny drop.

As to your fiddle, you need to take it to a violin repairer and have them fix it. I wouldn't dream of trying to lubricate the tuners of any string instrument. They need to hold the strings taut against the tension needed to maintain the instrument in tune. A friend has a vintage banjo uke which has fiddle style tuning pegs. One of the pegs worked loose and when she plucked the string the peg flew out, pulled by the tension in the string.