Yes. Within the next 45 days. If an NTA appears it appears, but filing quickly is your best bet to avoid that happening, for various reasons I won't bore you with.
Make sure to put a (brief!) letter in on the top, stating it is not being filed late, it is being filed because your prior I-751 was erroneously. denied.
It will be accepted.
Once accepted you will receive a new extension letter with a new receipt number, which is the one you use from then on.
Technically you can still travel now, but I would not - I would wait until you have filed a new one and you have the new receipt/extension in hand from that.
Now, here is the thing...once you have filed a new I-751, you are back in I-751 pending status, basically the same as you were before the interview. Therefore, after you file the new I-751 (assuming you do that fast enough), I would suggest considering also filing the N-336 for an N-400 appeal, or a fresh N-400.
This is because the denial of your N-400 was based solely on the denial of your I-751 (which they refer to as termination of your permanent residence, which is utterly factually and legally incorrect), which happened solely because your wife wasn't at the interview.
They can't deny a new N-400 without either denying your new I-751 or conducting either separate or a combo interview...so either way they have to review it. So if you file an N-336 or an N-400 AFTER you have filed a new I-751, you may well find yourself at another N-400 combo interview sooner rather than later.
And yes, you remain a permanent resident until an immigration judge says so. Try not to worry too much, it will get sorted out - eventually.