how long have you had your wii? 5-10 minute lag time on the wii time clock isn't that much too worry about; if you have got wiiconnect24 on, it could be adjusting itself according to the time servers on the internet. It is, however, possible your console battery could be losing power and might be in need of a replacement. Don't worry about the drive noise too much, I too get that here and there with games and sometimes it seems like the disc is getting spun quite harshly just trying to read the data but it is completely normal.
As long as the noise isn't consistent the whole time you are playing any game, then all is well. Some discs are a bit harder to read than others (due to various factors such as scratches, dust, fingerprints etc..) at times even though they are 'stamped' (the original ones anyway) and if using 'backup' copies try using better quality disc or re-burn another copy.