Your question is a very important one, and it has broad application. In fact, since the applications are too numerous and complex to exhaust, we will, for the most part, only address the general principles.
The gemara[1] says that minors are believed when they attest that a house was checked for chametz. The gemara explains that this is so because, assuming bitul (nullification of) chametz was done, the problem of having chametz in his home is only rabbinic. Thus, we have our first guiding principle for deciding when one may trust a child: we may trust a child regarding a rabbinic law, but not regarding a Torah law.
However, the gemara’s case may be lenient for two additional reasons: 1. There is no known, pre-existing prohibition that needs to be rectified (lo itchazek issura).[2] 2. The child who is attesting has the ability to rectify the situation himself (beyado), since he can check the house for chametz.[3] The Rama[4] rules that a minor is believed only when these three lenient factors coincide, i.e., the law is rabbinic, the prohibition is not known to have pre-existed, and the child can rectify the situation himself. Many[5] take issue with the Rama and claim that when it is beyado, a minor is believed even regarding itchazek issura. Tosafot[6] requires that the child himself will be relying upon his own testimony (e.g., eating the food), and some poskim prefer that we rely on their checking only in such a case.[7]
A specific case where poskim “hammer out” the issues is the question whether a minor is trusted that he performed tevillat keilim (immersing utensils). The Shulchan Aruch[8] rules that a minor is not believed. The Taz[9] explains that this is because tevillat keilim is a Torah law. A major machloket Acharonim exists regarding tevillat keilim of a glass utensil, for which there is only a rabbinic obligation.[10]
The situation regarding checking food for infestation really depends on several factors. Since there is no knowledge that a problem did exist, there is no issue of itchazek issura. On the other hand, to check many foods properly requires concentration and toil, which may challenge the child’s capabilities and credibility. We suggest the following. If the likelihood of a problem is not very high, a child can be believed since there is only a rabbinic requirement to check. It is best if the child will also be eating from the food. In certain cases, where the likelihood of infestation causes a Torah requirement to check, a child is not believed.
Of course, any leniency must assume that the specific child is fully capable of doing a proper job.