Will it be a problem running both avast! premier and Emsisoft Anti-Malware?
Yes, that will cause problems up to system crashes.
But you could use Avast together with Comodo Firewall or Online Armor Free(also from Emsisoft) 
And if I will add avast services to emsisot anti-malware white-list and the same with avast?
That would not really do anything cause their whole real-times are getting in their way.
Best is to have one that is build for running together with an other AV, like Malwarebytes PRO.
Yes, they will work together (direct from Emsisoft) however, 2 A/V programs WILL slow you down!
Sincerely,
J.R. “AutoSandbox Guy” Guthrie
“At this point in time, the Internet should be regarded as an Enemy Weapons System!”
Read this about two resident a/s’ http://www.bleepingcomputer.com/forums/t/260844/two-anti-virus/#entry1441638
You should never have two resident anti-virus running at the same time. 