Negotiation timeframe?

Calm down. It isn't passive-aggressive or unprofessional. It is negotiating strategy and reality. After your initial offer was made close to the weekend, the seller no doubt wanted to go through the Sunday open-house cycle attempting to parlay the fact that he had an open offer into higher offers from others who expressed interest, if any such buyers emerged. That evidently didn't happen, so the seller counter-offerred. That should have indicated to you that no one else was bidding at this time. Your second bid could be formulated accordingly. You might do well to take your own time when bidding and not appear too over-eager and willing to pay a higher price.

There is no advantage to you in rushing this part of the process--within reason of course. If you really need fast replies, convey a deadline for your offer, or convey that you expect a response within x hours/days or you will consider withdrawing the offer. I don't especially see what the long-range advantage of that is, but you can do it. If you don't want them to "use" your offer at open houses, then make the offer on a Monday and withdraw it by the weekend if there isn't a deal. Truth is, I think it is better to just let negotiations take the necessary course and if another bidder emerges, fine. Another apartment will come along. Even if you reach an agreed upon price, by the time you complete due diligence and sign the contract, another open-house cycle will likely have passed and the seller could always accept another bid until the contract is signed.

Seriously? This is normal practice?

I too thought they were using our offer as incentive to others at the open house..... that being said.... many brokers have thrown the words "we have an offer" around...and I never really believe them. There's no way to know if there really is another offer waiting in the wings, is there...... ?

Technically, a broker is permitted to say they have an offer only if that is true. Ethical brokers (and they do exist) abide by this. Do some say it even if not true or it's stretching the actual facts? Sure. You determine what an apartment is worth to you, develop a negotiating strategy and pursue it. If you don't, then you'll be following the seller's strategy. Like buying a car, most people do not enjoy the bargaining part of RE, but it's the way it is--say how much you hate it, get that out of your system, and then focus on the task at hand. That's my 2 cents.