I still do not understand your point because as you state there is no conflict between the two agreements, and further there are no pair countries involved that mutually agreed to the ICC:

- Diplomatic Immunity (through various treaties): Countries that participate will respect diplomats - ICC: Countries that agree will participate in ICC judicial process

From what I can tell, you seem to be under the impression that there's some conflict here. If that is your position then you are wrong. A country can both simultaneously respect foreign diplomats and work with the ICC to ensure that local citizens are held accountable in the ICC.

BUT, a further point -- international law can never be binding. It's between sovereign peers, and is based on the concept of reciprocal benefit. International treaties give the participants some benefit in exchange for something else. This has to be the case because there is no superior entity to arbitrate violations of the law. If you don't keep up your end of the bargain, you risk the other participants not keeping up their end of the bargain.

This is, for example, why having the top US officials committing war crimes is bad -- it's not because some superior nation will inflict justice upon the violator (because no such entity exists) but because other signatories have no legal obligation to not commit war crimes against us (although, many people are morally opposed to most war crimes and wouldn't commit them anyway).

A further note about your PS, which seems unrelated to the topic is that bombing isn't itself an invasion (it may be part of one), but for my opinion I think that killing people without due process is bad and should be a last resort for defense.