If you means tittle of your post then yes it will cause many problems including you will get less traffic from search engines
Yes, If you're ranking for that page. It will cause problem like ranking fluctuation coz Google takes time for crawling and indexing a page(new or updated).
For me, if you fixed your title tag then it would be better to avoid the problems like the Ranking of your website and search engine traffic.
I think No1 is correct, No2,3 is not correct. Changing title will not hurt anything about Google penalty algorithm, and Index. You can have the post reindex by submit in GG webmaster tool, at Crawls section.