Since you know it is simple job, then you can do in future. Part of learning process.

Yes, the charge is up to the plumber. You just need to call ask ask but many cases also they need to come to look at the problem to give quote and you will get charge for that, but you can ask for estimated price range if the plumber is willing to estimate. You can use as reference to compare with other plumber.

I suggest that you Google YouTube to find out how simple DIY fix can be done. If you think you can do it, then you can try. If not, ask for quote. If your DIY is not successful, you can always call plumber