Assuming this is an arrangement with a single person; whom you probably know to a certain informal degree; and they are not in the regular business of renting out their airplane.
The easiest solution is to have them add you to the policy as a named and insured pilot. You will in turn, pay the resulting premium increase. Generally they can put several people on the policy without issue. You need to review the policy but in the vast majority of cases, a pilot specifically on the policy is protected against subrogation. You then need to decide if the policy limits are enough for yourself and act accordingly. It's important that the relationship be generally casual, non-commercial, and not profit oriented for this to work out. In other words, covering the costs.
I will warn you that flying under an "OPW" or open pilot warranty has more risks. In certain cases, your interests may not be protected.
Again, I can't stress enough, reading the actual policy will tell you exactly what is and is not covered.If this is not possible, you can buy non-owner coverage through avemco and many others. Read the limitations, and if you accept the cost go for it. The good news is it covers most any non-owned/loaned/rented/borrowed plane. The bad news is its stupid expensive.
Your decision to carry insurance and how much is a business decision regarding your particular current and future personal and financial situation. In the end, you owe it to whoever is kind enough to permit this arrangement to ensure their assets are protected; whether or not you need to do so personally.
Regarding your other questions, this type of arrangement would not normally change any maintenance requirements. Of course, you still need to ensure its airworthy as PIC like you would any other plane.
I have seen this type of arrangement work before. It is not overly common, but over the years there have been individuals who have built a rapport with inactive owners and agreed on something mutually beneficial. The arrangements vary, but typically it's more than just cash for time.
Welcome to BCP. Not the usual first post here, that's for sure

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