1999 Miata check engine light
 

So my check engine light came on and I don't remember the code, however my mechanic sad it was the EGR valve/sensor. Light stayed off for a few weeks and it's now back on. Car is starting to idle really low. Runs fine when I am drivinghowever when I stop, it idles very low at first and then the idl kicks up to 800rpm. Could I have a battery problem? It cranks slow when it is cold out.

Thanks