I extracted all tracks of an audio CD and tried to write them back to CD, but the writing application tells me that the CD is not big enough, even when using 700 MB CD-Rs. When I look on the harddisk I see that the files are more than 800 MB in size. Why?

700 MB is the storage space for data CDs. Data has a third layer of error correction which need more storage space. So sector size is 2048 bytes for data and 2352 bytes for audio. There are around 360000 sectors on a 700 MB CD-R, that is 737280000 bytes = 703 MB for data sectors. On audio CDs this is 846720000 bytes = 807 MB. This is why the files are too big to write them as data files, but it should be possible to write them as audio CD instead.