Having you changed your battery?
E-10 can occurr when your battery is getting low of power, and not enough power to move the piston road (E-6 mechanical error) also can be caused by lack of power battery..
Battery life is dependant on how much work the pump is doing the more insulin and cartridges changes will deplete the battery quicker than some-one only requiring to change their cartridge every 7-10 days etc..
If insulin (or mostiure) has got into the cartridge/piston compartment, it can't come into contact with motor or eletronic guppings of the pump.. You can with caution clean any mositure or insulin in the cartridge compartment with a lint free cloth, but you do need to take care though.. But before comencing ring accu-chek for further advice..
It may well be, that the insulin that went into the cartridge compartment is cause some stickyness, I would try taking out the cartridge, and shunting the piston forward and backwards, if any tried insulin on the piston thread should fall away, then if try to blow this out or gently tap to tap out the remments..
I would suspect E-4 is a totally separate thing completelty, occulsion errors, can be hard to pin point the actual fault, ranging from presure on the infusion set (I've done this a couple of times with my waistband being over the infusion set) The canular becoming bent, easier done with metal cannulars, more so with the 90 degree angle ones, as these can sometimes catch the underlying muscle and bending.. To a blockage in the tubing...
It take 3 units (if I remember correctly) not being delivered to build enough presure to set the alarm off (which for me is a lot of missed insulin) so BG's can raise about... As to your suggles of getting your BG's back some of this well be due to high IR at hgher BG's... If you are correcting a BG higher than 12/14mmol/ml it is a lot better to use a injection correction bolus then using the pump..
I tend to find that with anything higher than 12mmol/ml that a correction bolus combined with a TBR works a lot better to stablise my BG... I find the TBR sorts out my IR and helps avoids stacking corrections insulin..
You need to remember that with pumps you haven't got any long acting insulin in your system, and the quick acting will be 60% depleted at 2 hours mark so BG's can raise pretty quick and bringing it back to normal is also effected by the time factor of insulin not being delivered, which can effect the correction bolus as you may need to incorparated some of the missed insulin into the correction factor..
It is always unsettling when you get the first error alarms, mine was E-6 menchanical malfucntion, battery needed replacing (went half way through a cartridge change) But contact Accu-chek and ask to speak to the rep for your area if you feel that the customer services isn't settling your concerns..