Whis is the difference between 1) and 2)?

It all depends on the context, which is your big problem.

Well. Can sometimes performance mean function?

It can sometimes, and sometimes it can mean something else.

My function is my job, and my performance can mean how well or badly I do my job, measured against some standard or target.

Sometimes 'functioning' can mean the same as 'performance' and I believe that in a medical context 'fumction' can mean the same, e.g. impaired renal function.

Renal function is the function of kidneys, while renal performance is a (functional) demonstration of renal function. Here, "function" and "performance" cannot be substituted for each other.
Am I on the right track, Contrex?

In medical context, renal function can be measured. Example: Glomerular filtration rate (GFR) describes the flow rate of filtered fluid through the kidney. The most recently advocated formula for calculating the GFR is the one that was developed by the Modification of Diet in Renal Disease Study Group, (MDRD formula).

The severity of chronic kidney disease (CKD) is described by six stages; the most severe three are defined by the MDRD-eGFR value, and first three also depend on whether there is other evidence of kidney disease (e.g., proteinuria):

0) Normal kidney function – GFR above 90mL/min/1.73m2 and no proteinuria
1) CKD1 – GFR above 90mL/min/1.73m2 with evidence of kidney damage
2) CKD2 (Mild) – GFR of 60 to 89 mL/min/1.73m2 with evidence of kidney damage
3) CKD3 (Moderate) – GFR of 30 to 59 mL/min/1.73m2
4) CKD4 (Severe) – GFR of 15 to 29 mL/min/1.73m2
5) CKD5 Kidney failure - GFR less than 15 mL/min/1.73m2 Some people add CKD5D for those stage 5 patients requiring dialysis; many patients in CKD5 are not yet on dialysis.

Thank you.
But Contrex, the values of GFR reflect the performance of kidneys. In that case, function = performance here?

In this case, yes.

But I would never

never never

use "performance" to describe the function or the workings of the stomach, even though it's probably logically correct.

"Performance" has different connotations.

I agree.

How about describing the function of lung, liver, hormones...?
Never, never as well?

Not with "performance". I wouldn't.

If you put in an artificial heart, then you might describe its "performance".

But not a natural organ. Maybe that's just me, but I don't think it's good style.