On *most* toll roads, there is still a cash lane. But from what we've found, they do want cold hard cash, no credit cards. There are a few toll roads that do not allow cash or cards, they want transponder or they will mail you (or your rental company) a bill. Now, offhand on your list, I don't see any areas with those kinds of toll roads. Someone else may.
In San Diego, you will find that there are areas on I-15 of "carpool lanes". If there are at least 2 people in the vehicle, you can use those free of charge. If there's only one, though, you need a transponder for FastPass. When it's just me, or just my hubby, we just stay out of those lanes as we don't have a transponder (and don't need one). These lanes are well-marked, and can get in and out of them if you need to do so.
In areas of LA, the carpool lanes are not separate (as they are on I-15 in San Diego). Instead, they use the far left lane, and sometimes the far two left lanes, "separated" by a line and ridged pavement. There are ways to get in and out of them without crossing the ridged lines. Once again, these are for 2-people or more, but not to be used at all by single travelers.
I'm sure that other cities have both types of these roads, so you may encounter them elsewhere.
Sorry I can't answer your question about the insurance.