There are many things you can still do. Here are a few quick suggestions to start with:
Proper antenna ground. A mag mount is marginally OK at VHF / UHF, but there isn't enough capacitance at HF. The antenna needs a solid ground connection to the vehicle body.
Assuming basically no grounding from the mag mount, you have a sort-of dipole antenna, with the whip at one side and the coax+radio on the other side. This unwanted part of the antenna extends to include the microphone cord and the power cables which run all the way to the battery, the battery negative-to-engine block strap and finally the engine ground strap. This maximises the pickup of RF noise from the engine compartment.
If you must use a magnet mount, you should find a way to ground the outside of the coax properly, just as it enters the vehicle. Cut off some of the jacket, solder some braid to the coax, and bolt this to the vehicle. Or install a (SMA) connector, and mount a F-F barrel to the vehicle. Ferrites on the indoor section of the coax will also help.
Vehicle Panel Bonding: The next step is to bond the body panels together with earth straps - first the hood, the box (might not be connected to the chassis) and then perhaps the doors. This blog post shows some photos and gives some more hints. I think the straps don't need to be as thick as they show (this is not for lightning) so rather use a few small straps with self-tapping screws. Clean off the paint first, and re-coat after assembly for corrosion protection.
Panel bonding will help with both the performance of the antenna, and the pickup of interference from inside the vehicle.
Ferrite beads on the power cables: to reduce the transfer of noise from the engine you can try clipping some ferrites over the power cables. Important to clip over both + and - leads, the ferrites won't work if they see a large net DC current flowing through them. You could try beads both ends of the wire. If you've tried a separate battery then perhaps this isn't the most important step.
Noise Blanker: The spark-plug noise will be hard to eliminate completely. Most radios have a NB feature which mutes very short impulses, without spoiling the sound overall. If you have spark plugs, you will need the noise blanker.
You don't describe the noise in detail - I'm assuming it is ignition noise, which is most likely, but there can also be alternator noise and alternator whine, and more general interference from the vehicle electronics.