The alloy calipers will expand more than the pistons so could explain why the wheel feels looser when it all gets hot and tighten up when it cools down again. This itself indicates something is amiss. The fact that the pads have worn unevenly also indicates something being wrong and needs fixing. Continuing to ride the bike with binding brakes will cause premature wear to the pads, discs and your nice new tyre, and if very bad can cause the disc to overheat and warp. There is also the safety issue of the brakes not working at their best as well. To do the job properly the caliper and pistons need stripping, cleaning and new seals fitting if needed, and the caliper sliders will need cleaning and re-greasing. If you feel confident about doing it yourself then have a go. I think there's plenty of info. on here to help but as it's a job that needs doing properly for safety reasons so if you're not too confident have a competent mechanic do it for you. I can't help thinking that your quote for £20 is too cheap and would worry that the job will not be done thoroughly.
