I have a question.I have to send research proposal for PhD to different universities.How do i ensure that it will remain plagiarism-free until evaluation by all the universities?

Use Turnitin. It may help you I think.

You mean, how do you stop other people stealing your ideas? You can't.

The only way to protect yourself is to retain emails in which you sent your proposal to specific people. But be mindful that they can always claim they had a particular idea already. And that might genuinely be the case, as it is rare for someone to come up with something completely and totally novel.

I would recommend not sending detailed proposals to people unless you've already established at least a small connection with them (i.e. don't send stuff with the first email you ever send them).