FHS mortgage questions

So, our landlady told us yesterday that's she's selling the house, and we've 6 months to move. Not ideal timing, as we're not ready to buy yet.

She has given us first refusal on the property, at €355k. That seems in line with two other houses that sold this year, though we may try get her down a bit, saying she'd lose money on rent while trying to find a buyer, list a few problems with the house etc...

We don't have the deposit saved yet, and probably won't get approved for a €350k mortgage, so looking into the FHS. Seems like that can make up the shortfall, at the expense of 20-30% share in the house. Ideally, I wouldn't do that, but we love the house, friends and family all nearby etc... and are willing to deal with that.

Am I right that I would go to the bank and look for approval for a mortgage for the house price - minus whatever the FHS would cover (i.e. €355k - €105k (30%) = €250k).

Also, am I better looking for a single or joint mortgage? My wife is a homemaker atm and has been for a few years, so no earnings to show.

Finally, any downsides to applying if we're not 100% sure we'll get approved (i.e. is there a wait period after being rejected)? We've a talk with a mortgage advisor next week, but tempted to just apply now.

We've to tell the landlady if we're interested in this by Dec 31st to keep the price offer, so kind of scrambling atm.