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Grunos, the preamble provides that each clue is "an algebraic expression for the value to be entered". As a non-mathematician, I mentally inserted an equals sign before each clue. That seemed to work. I hope this helps.

Yes. It's a square number.
It is a tough puzzle, but it's a rewarding one. Someone likened it to climbing a rock face, looking for one hand- or foothold at a time, which is a good description. It's just that finding each hold requires ingenuity and flexible thinking. And like climbing a mountain, there's a sense of euphoria when you get to the top.
Normally I do the workings for the number puzzles on the actual page in The Times, but I had to be a bit more organised for this one. If you use a spreadsheet, do the lower case letters in italics. I didn't, so I misread lowercase L (l) for uppercase i (I) and had to start again.

Mack that blows my mind that you can do the numbers one in the actual paper! Whenever I have done the numbers one I end up with about 4 sides of A4 with lists of permutations! 😂. Hence the reason for normally shirking them!

I use a spreadsheet for the numericals, so that I can play with calculations. I often use one for the more elaborate word puzzles too.

To the person who is attempting it: For me (who has major insights into squares), the solving is a deduction/elimination process where you read a couple of clues together and piece together the bits of info you have on each variable. Using a spreadsheet to keep yourself kosher is a good idea as someone said.

* sorry I meant NO major insights into squares

What a fantastic pleasure to finally get over the finish line. This is one of the best numerical and Listener puzzles that I have done - in about 60 years of doing them. Every time I got stuck I read the preamble again and found another step forward. Using the letters as a help to build the clue helped me to get more letters and so on.
Elap - you are a master, and I am in awe of what you presented to us and the way that you both led and puzzled us. Many thanks.

Thank you so much for that.

It would appear that the dozens of hours spent creating this puzzle have been justified!

Absolutely justified. What I loved was that a pencil, paper and possibly calculator were all that were needed. But the challenge never wavered. Many numericals become rather mechanical once the way in is identified. The way in here was not as obscure as some, but every step required thought, and it never felt a drudge. When I saw the final step I was stunned that it was a famous property I knew well, but you had avoided the obvious exemplar. I felt very stupid!

I can't improve on the descriptions given by n00b26 and quisling and await the setter's blog with interest. Your effort was far from wasted. What a joy.