You are supposed to check placement and residual as you mentioned before instilling anything into the tube. It's a far from fool-proof verification. Mostly good for determining residual. But we have to do it any way. Tubes can and do migrate or perforate. If they perforate, you are going to be looking at classic "surgical abdomen" symptoms. They also can also obtruct (partially or fully) the pyloric sphincter. With that you see large residuals and vomiting.
After re-insertion, the stoma is often red, irritated, possibly swollen, especially if the tube was accidentally pulled with the ballon intact or there was much leakage of gastric contents. The stoma and peri-stomal area can get infected. Fungal infections are very common, but bacterial infections do occur. If the area is very red but not infected, something like Bacitracin ointment may be ordered to protect and hopefully prevent infection. The usual antifungal creams can be ordered and for bacterial infection, Bactroban is usually ordered. Systemic antibiotics are rarely necessary. Cultures are rarely ordered. Assess and follow facility procedure as you would for other topical infections.
As far as I know re-insertion of G-Tubes after the site has healed is within the scope of practice for LPN/LVN's in all states. Many facilities have policies against it. Some LPN's weren't trained in school to do it. It's best to do as you did and do any procedure yourself that the LPN/LVN doesn't feel competent to do.
We are both referring here to the commonly used "Foley-type" tube which is not surgically inserted. J-Tubes and most PEG tubes must be re-inserted by the interventional radiologist. Mic-Key buttons may be connected to a GT or a JT. If connected to a GT the parent may change it (or an LPN/LVN). If connected to a JT, it is also re-inserted by the interventional radiologist.
Many things on the NCLEX-PN state "helping the RN' because post-graduation training or certification is required in some states to perform the procedure independently. A prime example is insertion of peripheral IV's. It is within the scope of practice in most states for LPN's to do this. However, the training requirements vary from employer sponsored training to an additional state certification/license. The NCLEX-PN is based upon the skill set that expected of a new grad throughout most of the country. A PN student may check with an instructor as to whether GT re-insertion is a generally required skill where you are.