There's no 'always correct' answer for that. It's a fairly good idea to place antennas as far apart as possible/practical. There can always be some interaction between antenna so the idea is to minimize that interaction as much as possible. Distance is a good way of doing that. If that scanner is going to be monitoring frequencies in the same band as the transmitting antenna, then there will be MUCH more interaction, possibly destructive interaction. Distance between antennas in that situation needs to be -much- larger, and will not assure something doesn't get too 'upset' to work anymore.
As far as mixing/matching antenna parts, it's better not to if possible. As you suggested, there can be differences that are not readily apparent, who knows what would result. One aspect of that is that receiving antennas tend not to be 'exact' as those used for transmitting. Receivers are just not as 'picky', sort of.
No matter what bands of use, I honestly don't think antennas within inches of each other is a good idea at all.