Why are you manually removing the points one by one (and resizing the array), if we already know that that all points *are* selected? Wouldn't it be better to just do a:

MEM_freeN(fcu->bezt); 
fcu->bezt = NULL; 
fcu->totvert = 0;
i = 0;
changed = true;

Potential numerical stability issues with large numbers (e.g. overflow, etc.)

Mark any unchanging variables as const

See comments on the other function

1. You might as well make the last arg float P[5][2] to make it explicit to both programmer + compiler what the bounds of that array are

2. Is compute_keyframe() exposed/used outside this function. If not, mark as static. If it used outside this file, the naming is ambiguous.

General comment: Follow the style guides on the wiki :)

Any reason why this needs to be at the top of the function?

Suggest to move after the 3 defines below. In general, try to limit definition of variables to the top of blocks only (i.e. try to not interleave code + definitions too much; if you do define variables in the middle of code, try to group those definitions together, to make it easier to find them).

Why change this?

Group these assignments, e.g.

prev->h1  = prev->h2  = HD_ALIGN;
next->h1  = next->h2   = HD_ALIGN:
// ...

Why the duplication of code with the previous branch? Just keep all these handle recalculation bits outside of the if/else blocks.

If however there is some difference between the two cases, please make sure to clearly label them, so that
it is easy to tell whether something was intentional (i.e. a critical difference) vs an accidental typo.

Is this used anywhere else?

Why are there two functions that are basically Copy&Paste with some indices changed?

Somehow this part with different t for different coordinates feels iffy - a bezier curve is a 2D curve parameterized by common t after all.

Replace vs insert is determined within insert_bezt_fcurve. This is logic duplication and potential error source. Also, in this function it is already possible to detect replace vs insert by comparing oldTot and fcu->totvert - that's what oldTot is for.

Don't change handle types arbitrarily. As I see it, the usefulness of this patch is to be seen in correcting manually set handles when inserting a key between them. It should never force insertion of a manual key instead of auto, unless possibly when inserting between two manual handles. If at least one of the adjoining handles is auto, the inserted key should remain auto.

The reason for this is that non-auto keyframes are a big liability: once they exist, it is impossible to fully control the animation without the use of the Graph editor - adjusting the key via dopesheet or insert keyframe will break smoothness of the curve as the handles won't accomodate the change.