For the most part, the topic's answered by the gameplay section for those games on the wiki. It might be missing a couple small details though.
Pretty much. The only game I can think of where you suicide to lower rank is Battle Garegga. Everything in Touhou is actually possible to dodge at max rank, with the (iirc anyway) exception of Mima without ReimuA. But even then, there's no reason to kill yourself beforehand.
Armed Police Batrider has a similar gameplay, with substantial differences compared to Garegga's (APB doesn't use the option formations as intensely as Garegga uses, in fact only the Garegga ships in APB can switch between option formations; Garegga doesn't have APB's aura attacks and no-shot charge up attacks).. Garegga's rank is more affected by shooting than APB is, while in APB, collecting items (options or shot power items) influence rank more than it does in Garegga, etc.. (APB has a maximum of 3 lives, Garegga has 5)
both games are made with this mechanic in mind (unlimited score-based extends, suicides which reduce more rank the less lives the player currently has, suicide to lower rank -> score to gain extends -> suicide to lower rank -> repeat ).
Much has been said about deaths being the way to lower rank in EoSD, but most people tend to forget to not make the rank angry needlessly. (it's a very important detail to remember, in games such as Daioh, in which it's believed that point items will raise rank considerably and not reward the player accordingly. I also lost a lot of time trying to make savestates before I knew that I shouldn't get purple power items, which ruins runs and savestates made after you picked them.)