Modern frequency synthesizers can easily do a few Hz step size up in the gigahertz range and be within a few ppm. That doesn't really matter that much though, since modern radios (at least these digital ones) are built as SDRs. They can shift the signal around and select whatever band they feel like.
Sure, but that's on the receiver side for carrier recovery. Wouldn't it be problematic if you mashed a bunch of channels/allocations sufficiently close together that they started wandering on top of each other?
Modern DAB/DVB receivers are usually zero-IF, the wanted band of frequencies is mixed down to baseband and filtered with a sharp cutoff Surface Acoustic Wave filter then sampled with a fast ADC. Selectivity is then dependent on DSP.
On the transmit side, you have to carefully combine the outputs of your various transmitters with a complex filter network, which at high powers looks something like:
