Distance is the first and biggest issue. Most PIR sensors will have a reliable range of about 20 feet, at best.
On demand polling of the sensors isn’t how Z-Wave PIR sensors work. The sensors report their state changes(immediately) tripped/untripped. Polling intervals are hours long.
Can I schedule the sensors to be armed every 3-5 minutes, read any events generated and then disarmed them, again to be armed 3-5 minutes later?
Sure, you could, but it would be completely pointless. The Z-Wave sensors will report their state changes(tripped/untripped). You'd then configure the controller(Vera) to (not)take action based on that and possibly other criteria/logic. Armed/Disarmed is a logical state, it doesn't turn the devices On/Off or physically affect them in anyway.
I could spread the arming/disarming schedule across the 3-5 minute interval, if getting events from all 40-50 sensors at a time is no possible.
It would not be possible to poll battery operated sensors with any reliability, if that is your goal. Battery operated devices sleep and do not respond to polling for hours at a time. Vera can handle the reception of 50 trip events within a couple of seconds. You won't likely get 50 simultaneously because the Z-Wave network would introduce some latency, but Vera would be able to receive and handle them all within a few seconds.
P.S. I am doing this more as a personal initiative, so need to keep the final setup under $2-3K. Bringing an consultant into picture would easily cross that.
I meant alarm company sales consultants. They're unlikely to charge you, as IT consultants would. But, project cost would likely be MUCH higher than you want to go, especially since most alarm companies make their money from monitoring, which you won't want.
Assuming Z-Wave sensors, which again are not suited for your requirements, you’ll need far more than one sensor per room and numerous sensors for large rooms. You’ll also definitely need repeaters(wired devices), as battery operated sensors do not participate in Z-Wave mesh routing.
4(sensors)50(rooms)$35(per sensor)=$7,000 and rooms as large as you describe would require perhaps a half dozen sensors or more.
Frankly, I think that the meeting room in use scenario is much better addressed by company policy and groupware(Microsoft Exchange?) resource mailboxes to schedule and reserve rooms.
If I absolutely had to use alarm technology for presence detection, I’d suspect that laser grid/plane would be the better option for your situation, but that’ll probably exceed the budget as well. Your max budget of $60 per room won’t get you much more than a mailbox license.