I'm not sure I know the answers to these questions offhand, but I did find this source (http://www.jasna.org/persuasions/printed/number14/breihan-caplan.pdf, see p. 20) which says militia officers "were supposed to certify that they possessed a landed fortune or a regular income" -- this certainly matches the (original) idea that the militia should reflect the structure of British society, which was based on property. Reading on in the article, it looks like the property qualification was relaxed considerably for the lower ranks.

I would imagine once the militia were disbanded, all officers lost whatever rank/salary/perks they enjoyed too, but I can't substantiate that. It would be interesting to investigate the situation in 1802-3. I can't imagine there was any half-pay as the militia only existed as an auxiliary force, but I do wonder if there wasn't a sum paid in compensation for any lost influence.

The War Office papers in the National Archives seems to have marching orders and militia returns (in WO5 and WO17 at a very, very quick glance) -- these might well help reconstruct where the militia regiments were sent. I don't recall seeing any detailed reference to the militia in the Monthly Army Lists, which is the only source I've found that details the District commands (someone might correct me on this, of course!).

I don't recall any recent studies other than J.R. Western, which as I recall goes up to 1802, but I'm seriously considering looking at the various auxiliary defence forces during the wars at some point in the near future. I will therefore follow other people's answers to this with some interest!