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I don't think the gift funds will be an issue, but the NSF charges are another story. Given the amount of fees, and the fact that they're recent, I would definitely expect the UW to be concerned and ask for additional information.
Not trying to scare you, but that's just my humble opinion.
They could ask for additional documentation to support the explanation in your letter. OD fees typically range from $30-40 per occurence, so that means that you had more than 10 overdrafts in less than a month's time, all occuring within one month of applying for a mortgage. It will not be a 'so what' for the underwriter. There are people who've been declined because of *one* NSF/overdraft. Regardless of your score, I would not expect an UW to let this pass on an LOE alone.
How long have you been with your bank? Would it be possible for them to write a letter stating prior to Jan-Feb, you maintained the account well and did not incur NSF fees? I think it would add credibility to the fact that the only reason you were overdrawn was because your mom was ill and you had to travel suddenly.
Okay take a deep breath...
The good is it is still an approvable loan, pending everything else goes smoothly such as the sale of your present home as an example. Your OD fees can cause you issues to the point of a denial. But once again breathe...
Since you are hoping to close towards the end of the month, that actually may help for limited expense if you were denied. So your game plan should be to figure out what you would be able to do for where you would live if things didnt work out for about 30 days. Rent a hotel room by the week? Possibly stay with friends and or family for a very short period of time? Figure out what you can do, and what you will have to do if for some reason you are denied.
You should be thinking about this anyway, since you have to sell your home first and would be committed to a contract with a buyer. So even if your loan is denied, what do you do tell the buyer your not selling? Im no lawyer, but I would think their is some repercushion.
Okay back on topic...
If you can find a place for about a month (if denied), and just reapply with a new Broker or LO come very beginning of April, most Brokers and LO's only require your last 2 months of statements, so your OD fees wouldnt be in the statements and since your home is already sold you would close in a fairly quick turnaround of 10-15 days.
Your biggest set back for yourself, is trying to have a plan B for a place to stay if things do not work as planned.