30%, 15%, 10%... Is that actually true?
It might eventually be the average observed at global scale, but to me it doesn't make sense to think like that.
30% of people (humans) will not mechanically click on the first result, while 70% will ignore it.
Also, a given number of people clicking on the first result (or any of them), will return to the SERP and visit other links too.
So yes, of-course the CTR you can observe for a particular page / keyword combination is highly depending of the niche, of the number of ads, news, videos showing before the organic results, or the accuracy of the results returned (you can rank first for a given keyword, but if the site title and snippet sounds off-topic, people will not click on it).
In fact I changed the title tag on a couple of pages a few days ago, saw a boost in CTR, and Google responded by dropping my rankings on those pages.
This is possible yes. Changing lot of titles at once, can be seen an attempt to over optimize them, or an attempt at reverse engineering Google's algorithm. So Google might not like it, yes. Long ago, it was possible to change elements of a page, and see the result in the SERP almost in real time (few hours and days), so, some abused of this, as always.
It's also possible your drop in ranking be linked to other factors, like algorithm changes, etc...
Be sure the titles of your page are not misleading are in line with the content of the pages. Don't use tricks to over optimize titles, they need to remain natural looking.