You mention wireless, although there is no wireless listed (eg, wlan0), so what are you expecting to connect you to the internet, wireless or wired?
Additionally, of the two wired connections that are listed, eth1 looks to be closer to connected than eth0 (it has an ipv4 address assigned); given that it is conventional to use eth0 before eth1, just check that you aren't making incorrect assumptions about which is which somewhere. And eth1 has an ipv6 address listed; probably best to switch this off, unless you know that you can go all ipv6, as having both often leads to confusion (and by confusion, I mean something like failure to look up DNS and/or poor performance doing so, due to waiting for timeouts). I believe somewhere in Yast there is a 'turn ipv6 off' setting.
Networkmanager tells I am connected to the internet...
Really, it doesn't. NM only knows whether you are connected to some other IP device and whether that has handed out a network address, and not whether that device has any connection to the internet. If the other device has handed out sensible looking addresses you won't be any the wiser until you try to use that remote device to connect, and then there are several errors that can occur.
When you say:
...nor can it ping to google with wireless connection...
I don't know what you did. Did you
or something more like
The second could work even if DNS is not working, and the first couldn't (dig for more information).