You've asked several interesting questions, and the simple (albeit not-very-helpful) answer to each question is, "it depends."
I don't know what the customs are in OR, but I know that in VA that sellers aren't allowed to require buyers to inspect a property, before submitting one's offer. The reason, that I stated what I wrote the way I wrote it, is that sellers in NYC usually require buyers to do the inspection, before submitting one's offer.
In Greater Cleveland, there's a big difference between a city and a buyer's inspection. Some suburbs there require every home to pass a city inspection before closing, and Cuyhoga County sometimes might require a home to pass a city/county inspection before closing--even if the city/suburb didn't require the inspection. Depending upon where one buys a property in GC, one might end up ordering both. Yet, it's also possible to get that requirement waived in some cases if the buyer hires a certified engineer (typically a civil engineer), who's registered with the county, to oversee the inspection and any rehab (if necessary).
Whether or not you can terminate your contract without any repercussions will depend on how your contract is written. Assuming you have an inspection contingency, then yes, you probably can terminate your contract if you don't like the results of the inspection (also assuming that the seller is unwilling to make the necessary repairs or adjust the price). Nevertheless, you might want to have your agent and/or a real-estate attorney to review your contract.
HUD homes aren't any different than any other ones--at least structurally. You can think of HUD homes as federal government REOs. Keep in mind that whenever you opt to buy a REO that you're buying them AS-IS, so you need to do a thorough job with your due diligence to ensure that you don't end up paying too much for the property.