The reason why Paul had Timothy circumcised and not Titus is given to us; "because of the Jews which were in those quarters: for they knew all that his father was a Greek" (Acts 16:3). The issue with Timothy was that one parent was Jewish and the other Gentile, and so it would raise distracting questions about his ethnicity among the Jews. Paul used his Christian liberty, so that "unto the Jews I became as a Jew, that I might gain the Jews; to them that are under the law, as under the law, that I might gain them that are under the law" (1 Cor. 9:20). Paul did not compromised his principles with Timothy, but had rather used his Christian liberty bring an end to any distraction over the issue. What the Jews wanted was to reject Timothy because of his mixed background, so Paul had him circumcised! The case of Titus (Gal. 2:3), whom Paul did not compel to be circumcised, made Paul's position very clear. Titus did not pose the same issue. Both the parents of Titus were Gentiles, and Paul would not compel him to take up with Jewish ceremony. To do so would be a compromise of principles!
In scripture there is a difference between "believing", "believing in", and "believing on". If you "believe" someone, you accept what they say as truth. If you "believe in" someone, you have confidence in their character; i.e. it has to do with who they are, although it also includes that they are honest. If you "believe on" someone, they become an object for your faith, and this also includes both confidence in their character and in their words, but goes far higher.