First time PCs and Information Gathering - should we have done more?

Question

My party and I are all beginners in the RP world. We've started playing vanilla Pathfinder a while ago, and have come across some issues with gameplay. Our DM, who's also relatively new, has been doing a good job so far, but we keep getting stuck when trying to advance through the story. We are playing the Iron Gods adventure path.

In the backstory below, how could we have found the information quicker? Between the two times we go to the casino, we end up just poking around a dungeon, almost dying a few times, actually dying once, and not really getting any clues, just clearing the map. We're all very new, and don't know how to interrogate or interview people to get information. Did we do something wrong, or did we miss the point entirely? I'm fairly sure our DM was just getting impatient and put us along the story faster.

Aside: We've come across situations similar to this, as well, where we just end up burning that bridge and can't use that indented source anymore.

Backstory

An incident happened in the town. Essentially, all production had stopped in this blacksmith town, as their heat source had suddenly stopped working (it's a hill with fire blasting from the top, that's been working for dozens of years, till now).

Near the beginning of our adventure, we were invited to someone's casino with a small credit to each of us. We'd heard just prior that the casino owner may have some information we need, through gossip at a local bar. After going there, we start talking to people around the tables, drinking, and playing some blackjack. We tried asking questions about the owner and anything else that was happening in the town. All we really got was "There's a girl around here with purple hair that's been acting strangely.." and then the character wanders off without saying anything else.

Eventually we manage to learn that the owner is in the back rooms. But each time we tried to get information out of him ("The town's been on the fritz since [the incident]. Have you noticed anything strange going on?") he just skirted around the topic and tried to get into the back rooms to avoid us.

We leave, a few sessions go by that were relatively uneventful, and I think our DM got bored of us trying to deal with things that didn't exist and not find any clues as to what's going on with the town. He suggests we go to the casino again.

We do go back... And we start asking some questions again. This time one of our characters is brought into the back room. The casino owner corners us with some rogues and covers all the exits. We try to act dumb and just say "we're trying to fix the town, that's all that we're doing". The guy thinks we're an idiot and just tried to kill us since we were poking around in his business.

We get out with some lucky rolls and get the bar's attention. He lets us go as to not cause a commotion, and we catch him outside. He tells us some stuff that we finally find a use for, and off we go on our adventure again.

Answer 1

It takes a while to get ised to to role-playing and the likes.

You can always ask the DM if you can do a check to see if your character would know what to do.

Sometimes its hard to come up with words yourself for how to persuade someome into talking about something that has them evidently worried or scared for their life. However maybe a cleric or some One else has a history with this or etc.

It is a collaborative effort for everyone so have fun and sometimes that means giving someone a bonus due to their back story or lowering a dc If it feels necessary.

If your DM is ok with you making a check if you succeed come up with a fun role play thing for it.

Something like "I used to live under a tyrant and be struck with fear every day as I wondered of it would be my last, but you aren't alone. Talk to us we can help." Or some other thing that makes sense.

Lastly published adventures aren't perfect.

Sometimes it can be really hard to get on track when it comes to a published adventure, but a DM should try thinking of it as a guideline that can be changed to make it easier. Something almost like a scene you'd see in a movie or read in a book of the protagonists walking in on the wrong conversation, or being mistaken from behind as someone they might look like from that angle.

It comes with practice everyone has their own ways of doing things but don't be scared to talk as a group and brainstorm.

Answer 2

You mentioned you were ambushed into the back room, all exits covered. So maybe you could have found another way to enter the back room, maybe eavesdropped through the doors.

Maybe checked the guard's patrol and shook them a bit ?