Right of Abode stamp - actual terms and timelines

[MisterLysenkiy]

My wife has a British Citizenship for more than a year already (proven by original Naturalisation Certificate), however she does not have a British passport yet. Her application is on hold for 11 month so far by a policy team, who require her to change her maiden name to marriage name in her foreign passport (which is not doable) - this is well known issue here on immigrations board, but is not something I am going to ask about.

My questions are the following:

- we are going to apply for Right of Abode (ROA) stamp as it is a substitute of a visa for those who have ROA (incl. British citizens).
What are actual terms and timelines between the application date and the date wheт you've received your passport back with the stamp? They claim it to be up to 6 months (which is way too long), but I am interesting to find out the terms happened from real life cases.

- in case we decide not to do ROA stamp, then is it possible to travel back to UK with Naturalization Certificate? Will airlines consider it for boarding (as she does not have IRL BRP card or any visa and her second citizenship doesn't allow visa free to UK)? I know when you are in front of real UKBA border control - they're obliged to let you in, so we can easily travel back with it from Paris as there is UK border check right before boarding Eurostar (in case she has a valid Schengen visa).

- in order to be able to travel with only Naturalisation Certificate, she still needs a schengen visa as a spouse of UK citizen. So, will Schengen embassies consider her Naturalisation Certificate as her right to stay in the UK (like they would consider IRL BRP card)?