My tv does not support arc and i neither want it.
Why would you not want ARC/eARC? It's the only way to play Dolby Digital plus, DTS HD or any high resolution codecs.
Now the thing is if i bypass eac3 from stb which is connected to tv input via hdmi, the tv doesn't produce any sound (which as per my understanding should work, correct me if i am wrong).
No, it should not work. EAC3 can only work either through direct HDMI in, HDMI ARC or HDMI eARC. It won't work over optical for example.
Then if i connect my stb to avr input(through bypassing), the avr produce audio. I believe, this removes the doubt that there cud the problem the stb bypassing.
Correct, the problem is your TV and not the STB.
Now coming to the previous and main question, why doesnot my tv decodes and produce sound? Please help me in this regard. is there something to do with compatibility or my tv simply does not support eac3?
Your inbuilt speakers on TV do work with E-AC3 input, right? Your TV should support decoding E-AC3 as far as I see on the specs page. Try using the TV's inbuilt audio rather than doing passthrough to at least get to that stage, then we can go further debugging it.
What you want the TV to do is to pass through AC3(Dolby Digital) transcoded from E-AC3 if you're using optical as the way of connecting TV and AVR. If you're using 3.5 mm jack, then you need to convert it to 2-channel PCM signal. Your TV's sound output settings should have these options.
Now coming to my wisdom, i have read many times here in this forum that it is better to not connect stb and avr via hdmi as it cause damage to hdmi board.
That seems like complete nonsense to me. Your AVR is designed to handle way more power than what a puny HDMI cable can provide. HDMI is a data protocol and doesn't have much power in it, so physical damage by connecting to a bad source sounds impossible from an electronics viewpoint.
Modern HDMI ports are very foolproof and your STB did get HDMI certified so it won't send very high voltage signals there. And if the STB HDMI was so dangerous, we'd be seeing TV's go poof all over the news. Don't worry about it.