Hi Jason,
A couple of quick thoughts here regarding your questions...
1. Annual premium increases of 10% are fairly typical for the industry, but overall claims performance of their specific book of business really affects this number. As an example, if State Farm had greater losses than say, Allstate the prior year, you may see a rate increase for State Farm, but not Allstate. Rates for the standard market are regulated by the state too, so that is important to understand. An standard market insurer can't just arbitrarily raise rates to whatever they want. Their rates have to be approved and they have to show reason behind the request to raise the rate. They also may be required by the state to increase their claims reserve, which again... would raise rates. You can always shop around, but just make sure you are comparing the same coverages, deductibles, etc...
2. As for coverage amounts, many companies will require you to insure to their calculated replacement cost value of the dwelling. Many use Marshall & Swift data to determine building costs. (Think cost to rebuild/new construction costs.) For some investors, this works as if the house burnt down, they would want to rebuild. For some, they may just want to clear the lot and buy the property two streets over. The real question is, what cost can YOU rebuild for and is the coverage amount they are setting close or is it grossly off... For this reason, many investors choose to work with companies that are more investor-focused which often use surplus lines carriers....think Lloyd's of London, Allianz, etc. vs State Farm, Allstate, etc. With investor-focused programs you typically have more control over setting the coverage and limits to fit your specific business model.
3. Liability is the one area of insurance that I would never recommend someone skimp on. Typically the cost is low, so there's no reason to choose lower limits. Now, this is a worst-case scenario, but what if you have a fire and a tenant dies? Or a family dies? At that point, you may want a million or more in liability coverage for your per occurrence limit and 2 million for your annual. Or, think about if someone gets injured on the property and ends up with a life-long disability. Even if you "self-insure" the dwelling, I would never recommend going without liability. Those types of incidents are the ones that could threaten your entire business. Somewhat rare perhaps, but if they do happen, for the minimal premium cost difference... "no-brainer" in my mind.
4. As for the medical limit, that is typically utilized to reimburse someone for a trip to the Dr. or the ER that can be paid out as a "Good Faith" payment without having to go through an extensive claims process. Your main limit is what takes care of any larger injury...
5. Aside from injuries, liability also protects you if you damage someone else's property... think about one of your trees falling on a neighboring house or a fire at your house spreading to the one next door. Liability coverage can also help pay for the cost of defending you in a suit, if you are found to be at fault. That's just skimming the surface of a definition for liability, but should help you get a general idea...
Lastly, I'm sorry to hear about your opinion of insurance agents. Honestly, there are great and not-so-great representatives within every industry. I hope that you find someone that you can trust in the future. I can say that I have had my personal auto insurance through State Farm for decades and my agent and CSR's have been great. BP is a great place to find good recommendations, so I would encourage you to keep searching until you find an agent who understands your needs as an investor.
Though I am an agent, I now work in loss prevention helping investors avoid losses at their properties... so, no personal agenda in my encouragement. What I frequently find is that insurance can be a complex product and the frustration that consumers often feel is a result of a lack of familiarity or knowledge of the insurance product. Let's face it, who wants to sit down and read an entire insurance policy? Contracts are a central component of investing and insurance is just one of those contracts. Not a "fun" part of the business, but crucial to your success. Agents also need to better educate their clients too...
Hopefully some others will weigh in. Best of luck!