Also, if slaves did ever flee to Mexico, was it ever significant enough for Mexican politicians or the government itself to respond to?
Fugitive slaves fleeing Texas for Mexico was commonplace, though it isn't widely discussed today. The Mexican government opposed the institution of slavery and staunchly resisted forming any treaties with the US that would have called for returning fugitive slaves.
For example, in 1857, the same year that the US Supreme Court handed down the infamous Dred Scott decision, the Mexican congress passed a law declaring the immediate emancipation of any slave that set foot on Mexican soil.
For a slave living in Texas, all he or she had to do to be free was get across the Rio Grande, and there were plenty of Mexicans on both sides of the border willing to help.