EGR valve and broken exhaust

It would depend on the codes and symptoms as to if they were related as well as what was actually broken. The EGR pulls exhaust gases from the manifold just off the cylinder head, those gasses are sent into the intake to lower combustion temperatures in a bid to reduce emissions. Now if the exhaust issue was something that allowed fresh air into the exhaust that the EGR could then put into the engine, it could cause an issue. However that isn't real likely unless it was a broken exhaust manifold or something before the catalytic converter.
Do you know what the codes were off hand? Post them if you do and we can give you more information.

Based on those codes I wouldn't have touched the EGR. P0300 is a random multiple cylinder misfire while the P0302 is a cylinder 2 misfire. Both of those could be caused by the EVAP issue if the EVAP purge valve was stuck open. That could cause the other codes as well because the valve being open would act as a leak under test.
The EVAP purge solenoid is located in front of the battery and is an easy part to replace. It looks like the image below. There is an electrical connector on the top and then two quick connect fittings on the lines. It slips off the bracket, then remove the quick connects by squeezing the release tabs. Then remove the electrical connection and reverse the process to install the new one. Then if you don't have a scan tool that can run testing, have someone clear all of the codes. Then drive it and see what if any come back. You can do a blow test on the valve but they have a nasty habit of being intermittent. To test is simple, with the valve off try to blow through both of the line connections. It should block air in both directions. Even a small amount of flow can cause your issue as it will allow fuel vapor into the engine or air once the fuel vapor is used up and the vent valve on the canister is open.