re HIMARS/MLRS being sent to Ukraine
The US has deployed 4x HIMARS platforms (from pre-positioned equipment already in Europe) for training Ukraine personnel, along with 48x rockets/missiles (43-50 mile max range types) and associated support/communication/targeting equipment. US estimates training time to be 3 weeks.
The UK has an undisclosed number of MLRS platforms intended for Ukraine, along with an undisclosed number rockets/missiles of the M30A1/A2 and/or M31 GMLRS unitary warhead types. They are currently training Ukrainian personnel in the UK.
The US is currently pulling unspecified numbers and types of rockets/missiles from stocks, inspecting and preparing them for shipment. The US is also currently inspecting and readying an unspecified number of HIMARS/MLRS platforms for shipment.
NOTE that the US (with over 1200 platforms in service or storage) is the only country that can send a large number of HIMARS/MLRS platforms directly or indirectly to the Ukraine. There is the indirect option of taking advantage of the NATO ring system to move HIMARS/MLRS platforms and rockets/missiles from one or another NATO country to Ukraine, with US platforms currently state-side sent to replace those of the NATO countries.
The US also has a significant number (over 100) of HIMARS/MLRS platforms already deployed in Europe, along with a large stock of rockets/missiles. Some are pre-positioned, some are with one or another of the forward deployed US Army artillery battalions/brigades.
The other NATO countries that currently operate HIMARS or MLRS platforms are Germany, France, Italy, Greece, and Turkey. Norway has a small number of MLRS in storage.
Incidentally, Poland has just ordered 500x HIMARS platforms along with an undisclosed number of rockets/missiles.

A couple of nicknames for the HIMARS/MLRS are the "Grid Square Removal System" when used with cluster munition warheads, and "70 km Sniper Rifle" when used with the M30/M31 GMLRS unitary warheads.