1/ What is the best method to detect target in general? Is it radar because I see the most important and most advertised sensor on fighter is its radar

Radar is typically the best, but IR is getting better and better and the RCS of the fighters keeps getting smaller and smaller so we will see how it looks in the future.

2/ Why there is no AA missile with both IR and radar homing. Different IR and radar versions on the same missiles exist but combo on one missile seems do not. Will IR sensor and radar block each other? If not, I think IR + radar combo will help to identify target between chaffs and flares and simply the logistics and mission choice, isn’t it?

Cost and space, but having IR + TV would be interesting since small full HD HDR cameras only take up a few millimeters.

3/ In according to chaff and flare, I think TV guided can distinguish them because there is no way to fake target in visible light with HDR camera, isn’t it true?

It would only work daytime, but for daytime engagements I thinks its a fantastic backup.