to be honest the first thing i'd do is undo the changes you made and resize the windows partition back and see if the onekey now works if it does make 2 backup images of the drive so you can restore the drive to it's now working condition any time you like. at least one of those images i'd suggest should be on dvd's.
if onekey still doesn't work then use a linux live cd and fdisk (or any other disc manager program) and change the boot partition to pbr_drv (think this is the correct one, if not try each one in turn) and when it reboots it should automatically start the recovery program where you can return to a factory condition (same as using the onekey recovery.).
once everything is back to normal and everything is working again including the onekey and the backup images are made and tested as working, keep them safe, you can now start playing around with the partitions, personally i haven't ever seen a partition table like it, but believe the needed partitions for doing a factory restore are partitions 1: WINRE_DRV, 2: 260MB EFI, 7: PBR_DRV
3rd partition is made and used by windows os i believe, can't remember what for now.
4th is the windows os of course.
5th is the empty space you made by resizing.
6th i've no real idea but think is where lenova put all the extra bloatwhere software they install along side the windows os.
yes the 24gb drive 0 is a separate ssd, now again i have no idea how it is setup and used by lenova but would presume it is just used as a cache drive like you said.
i don't know how you plan on deleting the partitions and installing win 8 but would assume you have a win 8 dvd to do the install.
anyway now you have a way of restoring the drive with the images, so yes you can go ahead and delete any partitions you like, all would be my choice, without causing any problems (not the case before making the images.),
install win8 and then install your linux system for a dual boot system.
hope that answers your questions and helps you. 
