I expect you will need a separate foundation for the stove, but you may not need one for the bench. If the floor joists run perpendicular to the bench, and are not so flimsy that you are concerned about the existing floor being bouncy, and the bench location is near an outside wall or main support beam, they
should be able to support the added weight of a cob bench. At most, you might need to add a beam under the joists in line with the bench and support it with a few piers.
If you need to cut out joists for the stove foundation, I would double up the remaining joists on each side of the new opening, and add a double header joist to carry the load from the cut-off ones to the doubled ones. Cut the joists back
enough to allow you to add the headers without choking the opening.
The amount of new foundation you need to add depends on the character of the soil under it. What do you have? Sandy, loamy, clay/hardpan, rocky...? If clay, what kind? There are expansive clays that swell a lot when wet, and those are tricky. There are other clays that are almost as good as bedrock for support.
Does the crawlspace freeze in winter? How deep is the standard frostline in your new area? What is your microclimate? (Warmer or cooler than average, drier or wetter?)