Will it damage the suspension if I leave the lockout knob engaged while trail riding on mountain biking paths?

be specific, what fork & how big a drop?

I don't know what you mean about drop but it's a RockShox Recon Silver with 100mm of travel on my Marin Rock Springs 2. Must of rode it 7 miles before I figured out that the lockout was engaged.
https://www.performancebike.com/shop...lusive-31-7055

It's not great, and yes it can damage some suspension designs, but the Rockshox Silver has a TurnKey damper which has a blowoff so it should be OK taking hits while locked out. In extreme cases you can still damage the damper. I would recommend not making a habit of it, if only because suspension is helpful descending off road!

Well what are the signs if the suspension is damage?

In the case of the compression dampener, it would be that it would no longer lockout and whatever compression damping control the fork offered would no longer work. It could also alternately impede the flow of oil in an uncontrolled way making the fork move slowly in both directions.

If your fork feels the way it did before it's fine (it's probably fine.)

I've noticed a barely noticeable squishing noise coming under the lockout knob; is that something to worry about?

That sounds pretty normal. I wouldn't worry about it.

Can you overtighten the lockout knob when locking out or doing the opposite? I ask because I took my bike to LBS for an unrelated matter, and the lockout would not engage, and I think the suspension was a bit spongy. The bike mechanic did his magic and now it works fine; only difference is I don't need to turn the lockout knob 180 degrees just 90. I think he said something about it being overtighten which is why I ask.

Sounds like a good question to have asked the mechanic who worked on it.