Considering purchasing a brick farmhouse in mid-Michigan built in 1885. There are large visible cracks in the foundation. Anyone have thoughts on the cause and possible repairs?
You need to get a professional home inspector onsite. He should be capable of telling you whether these are cracks of structural significance or not, and discuss remediation measures (not cost thereof).
It's amazing to me how residential construction is so over designed. Your pictures clearly show how the corner of the foundation has cracked and fallen away from the structure. Obviously, it's not "needed" to hold up the walls of the house, or it would have fallen down by now. (Are there large cracks in the wall on the other side of this area? ...No, probably not.)
These stone foundation systems are constructed by mortaring stones together. However, no reinforcing steel (rebar) is used. So, the foundation can withstand vertical loads placed on it, but it can't withstand "soft spots" in the soil. When the soil settles away over time, it tends to crack due to the weight of the foundation.
While that portion of the foundation is not structurally required, it's unsightly and will continue moving (sinking) away from the house. It needs to be repaired. There is equipment that can "raise" portions of a foundation. They inject special foam into the ground that pushes it up and into place, then it is bolted to the rest of the foundation.
Also, good building practices would require a new pressure treated plate with anchor bolts that bolt the foundation to the stud wall construction.
The house has been there so long without any major problems, it's hard to say this is all mandatory. However, if not fixed, it will get worse. Soon, the crack will open up and allow small animals and horses to crawl in...and you don't want that.