I can answer 1. Use a bamboo skewer and wrap a thin cleaning rag around it soaked in your cleaner (bleach).

I usually don't have #2, but I always try to work my way from top to bottom (i.e.: dust tables before cleaning floors) and I always sweep before mopping. You may do the same and still have this issue - so not sure if that answer helps.

Toothbrush. But in tight corners I use an exacto knife to gently dig out and then the toothbrush. Actually, I really don't have much that needs this type of cleaning.

Funny how we clean. I always vacuum first because it seems to add dust to furniture. Throw rugs first with upright vacuum. Wood floors I use a small shop vac around corners/furniture feet, underneath. Then I clean by hand, can't seem to go the mop route as I like to rinse and dry too. After this, then I dust, it isn't thick enough to require vacuuming after.

The kitchen and bath are top down cleaning, which is the right way.