My 10Mbps egress link probably would not be able to queue so much traffic ? Thus having the 10Mbps policer on the ingress reduce the processing effort require by the router ?
Yes and yes. But for the second question, you might want to police on ingress for other reasons. For example, say your ingress might be forwarded to several egress interfaces, but you want to manage the aggregate bandwidth.
But how does the above link to policing ingress on the WAN side if my LAN side has a larger bandwidth then my WAN ?
It wouldn't if your only concern was LAN bandwidth consumption.
this will really depends if i am dealing adaptive rate traffic right ? I am dealing with udp video streaming that is not adaptive, doing an ingress policing will not help nonetheless, am i right ?
Again, it depends on what you're trying to accomplish. Some video streaming traffic is rate adaptive, but if you're dealing with traffic that's truly non-adaptive, yes, an ingress policer won't help you with that traffic, beyond what it might accomplish for other downstream interfaces, but it's unlikely all your traffic is such. Also for such traffic, if you drop any of its packets, for any reason, the source generally will not retransmit the dropped packets and the remaining packets not dropped might be useless.
Also again, for such a case, what happens if the upstream device egress port doesn't offer sufficient bandwidth? How does it differ from what the policer will do?
BTW, I've been in the situation where an ISP wouldn't provide QoS on their egress interface but I was able to, somewhat, manage ingress traffic using an ingress policy with class policers. I can tell you it works, although not nearly as well as an egress policy where you have queues you can prioritize.