1 missile every 2 seconds per 8-cell module sounds about right, actually. OTOH the entire bank of VLS modules can launch nearly simultaneously. I watched a YouTube video a few years ago where the rear VLS bank of a Ticonderoga launched something like 5 missiles from different modules in the space of literally half a second or less, all sequentially, but all within microseconds of each other. I'll try to find it. The universal VLS is probably only going to be able to achieve this rate when it's firing hot-launched missiles such as the as-yet unrevealed MRSAM. When cold-launching there is going to be hang time between ejection and motor ignition, which will probably prevent any other cell in any other module in the section from launching, especially if the missile performs a pitching maneuver during its hang time. So the launch rate per entire VLS SECTION will be on the order of 1 missile every few seconds, and this may depend on if they have to manually confirm that the missile ignited and left the area or there was a misfire or something. Whereas with hot launching the missile either leaves the area immediately or fails to ignite and stays inside its tube, the cold launched missile has to clear the area above the VLS bank before another missile can be launched. This is the downside of cold-launched VL systems. On a VLS bank the size of the 055 (with 64 tubes in the front section), it may be possible to cold-launch 2 missiles simultaneously if they are sufficiently distant from each other.
"Hundreds" is almost certainly an overstatement. One of the few AESAs that we have information on is the APAR, which is quoted to be able to guide 32 missiles during the midcourse phase and 16 missiles during the terminal phase. I don't know if this is total or per face. If total that means each face can only provide terminal illumination for 4 missiles at a time. It also uses ICWI, which means APAR doesn't even dedicate specific T/R modules to specific engagements but rather timeshares them among the engagements.
As for the Burkes and Ticos, there are 3 Mk 99s on the Burkes and 4 Mk 99s on the Ticos, for 3 and 4 simultaneous engagements at a time. However, these things work differently from AESA direct guidance. The SPY-1D guides all the missiles during midcourse while the Mk 99s provide terminal illumination. The Mk 99 only needs to illuminate the target for a few seconds during the end game to allow the SM-2 or ESSM to find and hit their targets, maybe even less than one second. After that the Mk 99 can immediately move on to illuminate another target. That means for targets that are closely grouped together (like a volley of ASCMs launched from the same fighter), a single Mk 99 can rapidly target each missile sequentially. Its limitation is its slew rate from one target to another. If it has to slew something like 100 or 120 degrees at a time to mark each of its targets, obviously the engagement rate will slow down dramatically. The SPY-1D midcourse guidance capacity is unknown but I would guess it to be in the several dozens range.
