I have the same combination on my bike. I only take the post out after rainy rides to remove sand, dirt and water. It's usually recommended to take the post out, clean it and lubricate it (just wipe it with an oily tissue) once in a while. I use Wako's Ruspene for that.
That can definitely happen, depending on the combination of materials and design of frame, post and clamp. I had it initially on my TImTanium frame with Thompson seatpost. The solution for me was a slightly beefier (500 yen) clamp.
Always use grease. The inside of the seat tube should be heavily coated with grease all the way 'round before you install the seatpost. [not carbon fiber seatposts, which easily can be damaged by seatpost clamps, too. If you have a stuck carbon-fiber seatpost, see suggestions later on this page -- John Allen] If you use enough grease in the seat tube, there is no need to grease the seatpost itself. (When you make a peanut butter sandwich, you only need to put the peanut butter on one of the slices of bread.)
Using some of the 'grit grease' can help if you want to increase binding power without overtorqueing. Seems a bit contradictory - however - the grease does help to prevent galvanic corrosion and long term sticking, while the 'grit' provides enough frictional component to keep the post in its desired place.