What is the typical resistance across the various terminals of a MC phono cartridge?

Assuming you are referring to a low output moving coil cartridge, depending on the particular cartridge the resistance between + and - for a given channel probably falls somewhere between one ohm and a few tens of ohms, depending on the particular cartridge. Some manufacturers include that information in the specs they provide, and some don’t.

The resistance between either terminal of one channel and either terminal of the other channel should be very high, essentially infinite.

HOWEVER, in the absence of good information to the contrary I would not recommend measuring any such resistances with a multimeter. My concern would be that the test voltage applied by the meter might harm the cartridge.

Regards,
-- Al

Pretty much EVERY MC cartridge provides this information in their specs.  I recall values ranging from 5 ohms to 40 ohms.  But I'm probably erring.

Applying DC across your cartridge is a big no-no and may well have damaged your cart (assuming you used a multimeter to try and measure the coil resistance)

Long discussion of this topic here in the context of some designs of demag circuits that may output DC
https://forum.audiogon.com/discussions/mc-cartridge-degaussing-demagnetizing

Having said this the current generated by a multimeter at the lowest resistance range measurement setting is probably <1mA, in other words in the same sort of range as that generated by the cart in use so you may be OK -- but don't make a habit of it