That's fine as far as it goes, but it's not as clear-cut as you seem to think.
It still seems so to me
* Is laser/missile/sand the only legal mix, or can you have two lasers and one missile, or two missiles and a sand, etc.?
You can also have laser/missile, laser/sand, missile/sand. You cannot have two of any one type, that breaks the different types in one turret bit. So no, you can't have two lasers and one missile, nor two missiles and one sand.
* Do you need extra gunners to fire the two extra batteries in a mixed turret?
Granted this bit is a little muddier. But it's not the key part about what constitutes a legal turret under the rules. In High Guard this bit (crewing weapons) depends on the type of craft (small craft, small ship, or large ship).
On a small craft (ships under 100tons) you need one gunner for each weapon beyond the first (which the pilot fires) and no gunner is needed for the sand. So a small craft needs at most 2 crew (pilot and gunner) with a triple mount turret. A double mount turret may need 1 or 2 crew. A single mount turret only needs 1 crew (the pilot).
On small ships (ships 100 to 1000tons), LBB2 crewing applies, so each turret requires a crew of 1, regardless of the weapon mix. Subject only to the possible option of instead declaring grouped turrets as batteries and then only needing a crew of 1 per battery (which may still be 1 per turret). But that is not clear as allowed.
On large ships (ships over 1000tons), LBB5 crewing applies (and mixed turrets are not allowed), so each battery requires a crew of 1, and turrets may not be mixed, and all batteries must be of the same factor.
* If you can fire a missile and a sand canister in between firing the laser, why can't you fire the two other missile launchers in a triple missile turret "in between" each other? In other words, why can't a triple missile turret be three different batteries? (Note that i'm not asking this question of triple laser turrets).
While I see no problem with firing and guiding a missile from the same turret, in the same turn, as you're firing away with a laser, and popping a sand cannister, my interpretation of why you can't (in HG) fire two or three missiles at separate targets in the same turn from the same turret is because the turret can only track and guide the missiles towards one target in a turn.
That breaks (a little) with LBB2 and the Multi-Target program rule, but we're not talking about LBB2. We both know how incompatible the two books really are despite LBB5 saying mixing is fine. The Multi-Target program rule from LBB2 is (presumably) abstracted into the LBB5 rules, in that it doesn't specifically say (but certainly implies by the computer table) that programs are needed at all but does allow targeting multiple enemy ships in a turn, by different batteries.
* If you can have two lasers and a missile launcher (or a sandcaster), can the two lasers be separate batteries?
As noted above I don't think the rules are unclear about not allowing two of any same weapon in one turret to be separate batteries.
One thing I might see being allowed is treating such as a primary and backup setup, so you are still within the rules of not having multiple same (active) weapons in a mixed turret.
For example, the TL15 fighter with two fusion guns idea: It would be a single battery factor 5 fusion gun, and if the battery/double turret were hit (destroying the single primary weapon) you have a second identical battery (single backup weapon) in that turret that can take over and still be a single battery factor 5 fusion gun. Until it is subsequently hit of course. At least this way such a design is not wasting the MCr2 and in fact needs only 2EP which is imo better overall.