I'm trying to setup a basic router with nothing special on it
(two interfaces, a default route, ...)

I'm able to ping to internet addresses, but I'm seeing arp-requests continuously trying to determine mac-address of:
internet addresses (google, ntp-server, etc...)

Someone can explain why routeros is trying to identify the mac addres of a host not in lan address space?

I don't want these arp-requests and tried to add a static entry to the gateway and put interface ehternet arp=reply-only
but routeros does not ping anymore to remote addresses, only gateway (can't find mac, and therefore does not ping -timeout)

Someone has solution to this issue?
Is this a normal behaviour on a tcp/ip stack?

what is your subnet mask on the internal interface? it should only be arp'ing for stuff in the local subnet and just routing everything else to the default gateway.