Hello,
ad problem 1), see
JoomSEF FAQ #18
ad problem 2), if the settings is "nocache" in JoomSEF, then the SEF URLs are handled by router.php file located in the component directory; if some of the URLs do not work correctly, the problem will be most likely in this file; the router.php is usually written by the component author, so if something is wrong with it, please, ask the author to check it
ad problem 3) this URL may be cached or created otherwise... if it is stored in JoomSEF database, you can always edit it manually
ad 2: With JomSEF disabled, the URLs work well. This is the reason why I assumed, the problem is located in JomSEF.