jemanden aufs Glatteis führen = to put someone in a difficult situation where every move can be dangerous, just as if you are standing on very slippery surface like ice (Glatteis = glattes Eis). jemanden durch Fragen aufs Glatteis führen = to ask someone difficult questions where a wrong answer can be emberassing etc. So the meaning of the example sentence is: He was very professional, and even though I tried to set him a trap by asking him difficult and tricky questions, he kept his calm and always gave good answers.