You may pray on that mat.
As for sending blessings to a non muslim when sneezes -this is not reported, therefore it is not permissible.

Can we offer the salah on a prayer Mat gifted by a non Muslim friend also can we bless u when a non Muslim sneezes.

Halal/Haram Matters | May 30, 2017 4:48 pm
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I just watched a video on youtube where a brother was saying that if someone mocks or insults Arabs then they also mocked the prophet because he was Arab, is this true? The brother also mentioned that something like that could take you out of the fold of islam.