Mazda 6 estate diesel 2006 - Mazda 6 not ticking over properly. - dbdako

I have recently bought a Mazda 6 and although I am overall pleased with the car and its performance, I am little concerned with a couple of slight problems.

The main one being that when the engine has got up to running temperature and the car is ticking over it will 'miss a beat' and the revs will drop a fraction every 10 seconds or so, this stops when I press in the clutch. I have read on other posts that there is a common fault with the fuel pump on the Mazda, but I have eliminated this due to it stopping when I press in the clutch (I may be wrong as I am no expert!), I was wondering whether anyone else has experienced anything similar and had managed to find out what the problem is?

The other problem, which maybe nothing, is when I am in 6th gear and especially when I use cruise control the revs seem to drop away quite dramaticaly and at any hint of a hill; and I find I am quickly having to drop down the gears to get the revs back, like I say it maybe nothing but I was wondering whether it may be related to the other problem that I mentioned.

Hope someone can help, thankyou.