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A final thought. As previously not a great fan of Playfair, I found this puzzle had just the right amount of difficulty (admittedly I used online assistance to solve). But to use two relevant codewords that applied to both sets of answers seems very clever or is my praise unwarranted and is it easier to compile than it seems?

Hello dear and wise solvers, apologies for being a cretin but I’ve only been at this listener gig for a while, and this is the first playfajr square encountered. I’m flummoxed and imo, it seems a bit of a ballache.
Presumably I have something very elegant to discover.

Think I understand the theory but absolutely no idea how to implement it with so little data. as it stands I have a full grid with only one definite letter for either 1a or 10d ( the B at square 35). Have tried reconciling the 50/50 letters into something recognisable (Plus likely alternatives that would make other words) but no joy. It seems one needs to make a leap of faith here, I’ve noticed the helpful weblink but still have no idea how to progress.
Basically: will somebody hold my hand please?

Hi n00b, I'm pretty new to these myself so no problem. I'm not clear from what you've said whether or not you might be getting confused.

For every clue, you should have one extra letter - these will give you the clues for 1 and 10. In addition, for each of the crossers with 1 and 10, you should have 2 more letters, one the initial letters for the answer to the * clue and one for the paired clue. I assume these are what you mean by 50/50 letters - ignore these for now, you can't make words from them.

Solve the clues for 1 and 10 (from the extra letters) then come back to the others.

Once you’ve got 1 and 10, you should be able to tell which is which (might be helpful to write them alongside their places outside the grid). Look for letter pairs that you know in 1 and 10 from either the *crossers or the paired crossers, and put as many as you can into the link provided using the corresponding letters from your actual 1 and 10 answers. Don’t fall into the mistake I did and put any old pairs of letters in - they must be paired off from the start of each answer. Try both sets of crossers - you should have 2 code words jumping out at you.

Once you’re happy with your 2 code words, build up their corresponding word squares and encode your answers to 1 and 10 for entry into the grid. Which is which? Only one will reveal the appropriate (short) thematic animal.

Hope that helps. Took me AGES to work through it all myself!

n00b - simond9x has explained exactly how you must proceed once you have solved the two names derived from the wordplay shown by the extra letters in clue order. As you cannot proceed without solving these - if you have trouble solving I see post 30 gives big hints...

Am stuck on first name. My extra letters start IRONE?NSTEADILL?....
I have 2 keywords: the first yields the second name but the 4-letter one gives garbage. I have answers to 17 and 30 but can't see the extra letter. A hint please!

17 and 29 - not 30!

Thank you SimonDx and Crates for your input and especially the time you took to help me with your posts. that makes some sense of my fuddled misunderstandings. Will crack on according to your instructions this evening. Much appreciated to have been given this nudge.

MarianneWhite, The extra letter for 14* is D (not N) HYE is antiquated high, Hyde was a bit of a character. 17 is NAURU but without last U (mostly) around anagram of SITE to make NASTIER, with the first U being the extra letter. 29 extra letter isn't L, it's Y. Terrapin is EMYS, without S (brief), preceded by IT (sex appeal). So, so far you have 'I RODE UNSTEADILY...' which obviously gives notice of an anagram, but beware that 'I' is not included. So anagram RODE after CH (an obsolete, dialectic form of 'I'), putting the whole of that inside SINGER, a sewing machine, and you end up with the anglicised spelling of one of the physicists who Hitler foolishly made unwelcome in Germany. And even people who have no interest in science will have heard of his cat, which you couldn't be sure was dead or alive.

Now look also at comment 7. for the last 4 letters of 1D you will have either DBAH or WBYM. Just key each of those in turn into the link, to match BERG. In one case you get 5 possibilities returned, in the other case only two. And in any case there is only one possibility which is faintly relevant.

I hope this helps.