Which one has a higher success rate between Infrared homing and Radar homing missiles, for air to air combat?
This topic is very broad, and there is copious material available on it. Therefore, this answer will be generalized.

IR targeting is very useful against jet engine aircraft, because there is a clearly defined thermal contrast in the thermal output of the engines. At close range it is low cost and low complexity compared to a passive radar targeting system. It is essentially, a point and shoot.

Passive radar targeting utilizes a more powerful, larger antenna on the deploying aircraft, and relies on the more powerful illumination which the targeting aircraft is capable of. If the illuminating transmitter is in the front of the deploying aircraft, then the aircraft's attitude must be maintained to continue to illuminate the target until strike.  This exposes the deploying aircraft to increased risk, and is avoided in close quarters.

Active radar targeting requires more on the missile electronics, but can work better in a point and shoot environment, and does not require the deploying aircraft to continue illumination of the target, allowing evasive maneuvers and pursuit of other threats.

The trade space between targeting methodologies is great and is dependent upon situational conditions. For example, at a long range, a passive radar targeting method can provide increased target strike assurance, and lowers the SWAP (size, weight and power) of the targeting package in the missile.

At close range, IR homing is often selected because it works well on close targets, has the best SWAP, allowing more weight for ordinance and motor.

All targeting systems have their disadvantages.  For example, while IR is very effective against jet engines, having the sun, or even glint can foil them, as can IR flares. Shooting against a ground target may not be as effective with an IR seeker, but it is done.  A passive radar seeker can be more effective against countermeasures, particularly when multi-static radar is employed.  In that case, several transmitters illuminate the target, from different aspects, and the passive receiver in the targeting unit can eliminate most countermeasures.

In the world of countermeasures, there are similarities. For example, IR Chaff is about as effective as RF Chaff, and does a good job at breaking target lock and inhibiting target acquisition.

Getting back to active radar, the SWAP is greatest for this targeting system, but it has the ability to act autonomously, similar to IR targeting. Antenna diameter is a limiting factor for good SN ratios. But this strategy is good for point and shoot, and works well at closer ranges.

With respect to kill rates, that is highly dependent upon the type of target and we haven't narrowed the discussion to aircraft vs ship vs vehicle, which influence the choice due to background radiation, reflections, etc.

The question is extremely broad, and coverage of the broad topic with multiple questions in this venue is limited.