~Petition signer must be registered to vote in the county for which the petition is written (may be living out of county if at college) and  18 years or older.  Democrat, Republican, Independent, DTS - all registered voters in county may sign.
They do NOT have to be registered to vote. They must be qualified to be registered to vote.
~Cursive or manuscript?  BTNM seems to think manuscript, though write in both if you can. They emphasized that the judge must be able to read your signature.   I’m used to seeing one column for your cursive signature and the next column for your name printed in manuscript.
It seems to me that it would be easier to forge
a name written in manuscript.  Not everyone, especially those with vision challenges, can write both in that small space.
What is your group doing?
Their signature needs to be legible. Do what it takes to get people to write a name the judge could read in the space provided.
~If Los Alamos cannot get the 2546 signatures  (as on BTNM map) on the referendum petitions, will the signatures we do have still count?
Your signatures will certainly count! We need 25% of the number of votes in the last election from 75% of the counties - totaling up to 25% of the votes cast in the last election (or about 180,000 signatures.)
~How do they calculate the number of signatures required (?) for each county?
See above
~When will the other 3 petitions be released?
We are waiting for the SOS to send her changes to these. HB 207 is still in progress.
~Petition - Size of paper? 8.5 x 11 only
Was the format mandated by the SOS?  Many petitions I’ve seen are on 11 x 17 paper, landscape view.
~Petition - Precinct?
I’ve never seen a petition that required a signer to write in his precinct.  Was that from the SOS?  Yes. Their precinct can be found here: https://voterportal.servis.sos.state.nm.us/WhereToVote.aspx 
~We had our Spring Tea and fundraiser on Saturday, so I did not get on the ZOOM meeting.   However, I was on last week.  I’m the one who pointed out that, on the petition they showed us, the last 3  signers forgot to write in their zip codes.  I also asked if the people running the petition drives could fill in the precinct numbers for signers, as was done on the sample petition, without at least initialing next to the precinct #’s they wrote in for signers. Yes, you can add the correct information if you have access to the voter database (which you should)