How safe is Java or flash and if it is installed should it be removed?

Flash is as dead as Yahoo! Answers.  You can't even download the player any more and there are no updates for it.  Any vulnerabilities in whatever version you have will not ever be fixed; and yes...Flash has been a security problem for at least as long as Adobe has owned it.  Get rid of it.  If you have flash videos that you want to view offline, I suggest a reputable free player like VLC. 

Java is even deader than that on the web, but that's not what Java is used for these days.  Java is needed if you run applications written in Java.  The game "Minecraft" is an example of that.  There aren't any particular security risks in Java that don't apply to any application you install on your computer.  If the application is malware (or has been corrupted by some virus) then you have a problem.  If not, you don't.

Java's "long list of security problems" are a dead issue.   The holes were in the web plugins and exacerbated by Oracle's attempt to compete with Flash for active browsing technology.  There were never any particular issues with installed applications.  (Any installed application can be malware, no matter what language it was written in.  That's what virus scanners attempt to detect.)  The Flash vs. Java web wars are over.  HTML5 won.

Both have a long history of security issues and exploits. Java is still being maintained so is OK to keep if you keep it up to date. Flash is no longer having security issues fixed and should be uninstalled.

Since you are using Windows 10, both will be listed in the "apps" if they are installed.

Going into "settings" and look for the "apps" icon.  

If they are installed, they will be listed under the installed program.  You can click on them and select "uninstall" to remove them.  

Flash Player was actually sunsetted early this year.  Microsoft sent out a patch that disables Flash so it will not play on your computer.  So even if it is installed, it can not run and can not infect you.

Java only works in Internet Explorer.  If you are running any other browser it can not run in them, so it can not infect you.