Doesn't sound like what I heard from the early episodes, which was pretty much nothing, but there was some back-ground used sometimes later in the series and I didn't picture it the way which you captured.
But I'm glad you delivered this. I missed it mostly then I guess.
Yes, I remember those blasts coming onto the ship in the episode you're talking about. There were some "camera-rocking" as well reminding me of old Star Trek.
Thank you for your answers and for taking it seriously without fuzz.

Not sure what you mean. The ambient hum of Serenity's engines were present throughout the entire series. Here's 12 hours of worth for your listening pleasure:
There are plenty of other sounds too. Like how we can hear Serenity's afterburners power down as she breaks atmo in both the pilot episode and film.
Or in Out of Gas, where we hear the explosion, then life support systems kicking in, and then nothing but eerie silence. No engine noise at all. I thought that was a subtle yet very effective way of driving home the helplessness of that situation.
As far as weapons go, I can think of two examples. In The Message, we clearly hear the concussive blast of Lt.Womack's warning shots, and in the film, we can hear the recoil from Mal's AA cannon reverberating through the hull.
It's all there. Maybe you just never noticed?

I know they had no shooting devices. Part of what I liked

Creative license. We still need to hear the dialogue. Plus, Serenity doesn't have any weapons.
You are sin.