can one verify with certainity that pool is not cheating? Can miner validate with 100% certainty that pool operator is not cheating like claiming that your share is smaller compared to other participants? i.e. telling you that your share is smaller than what it actually is.

I'm not telling about big percentage. But lets say can 5% difference remain unnoticed?
I believe that in the simplest, "spherical cow" setup that you could indeed know if you're being defrauded.
In my answer, I'm assuming no variance, no blockchain reorgs, really I'm not considering any variables which might skew calculation.

I'm also assuming you do know your own true hashrate -- that is, you count your valid shares yourself and can figure out what percentage your own mining is relative to the rest of the network.

Suppose you know that you should constitute for 10% of the network's total hashrate (you can learn an approximation of the network's hashrate by looking at the rate which blocks are discovered, and the current difficulty), but then the pool pays you less than 10% of the total bitcoins minted during a timespan (minus pool fees), then it's likely that you're not getting paid for all your work done on the pool.

Again, when the percentages are very small, or when other factors come into play like reorgs, selfish mining and natural variance, it will be increasingly harder to determine.