Is it advisable/necessary to use/discharge the batteries totally before
recharging, or can I recharge them when they are half used. They used
to say that rechargeables developed a "memory" - is that still true?

It never was. It was a con to persuade you it was your fault batteries
didn't last.

What did happen was that a process called 'Dendritic Growth' occurred where
a crystal-like thingy developed inside that shorted out the plates of the
cell. I built a device to destroy them (found recently covered in dust!).

I don't think modern NICADs of NIMH rechargeables do it any more though.

R.