Your purchase contract stipulates the terms of your agreement.
If you think that your Realtor is not trusworthy, call the office and ask to speak with the broker. Hopefully he/she will help keep things on track.
The settlement date should be stipulated in the contract. The concerns you mention are real and seriousl. As good as Trulia may be, consult with the broker or an attorney as soon as possible.
Let us know what happens.
PS>>>we do not offer legal advice....to protect yourselft, in most real estate transactions..."time is of the essence" so don't waste time., Resolve concerns now, not later...it's like a cavity...it only gets worse, is more painful, and costs more!