Yes, you should have the option to do inspections before you close. In California, buyers typically have 17 days from acceptance to do their inspections. If within those 17 days, the buyers decide that they don’t like what they find, then they can walk away. If the buyers do their inspections, then remove their contingencies, then they are committed to the property and the deposit becomes nonrefundable.
It’s extremely important for you to get your inspections done as soon as possible especially if you want to do any further negotating with the seller on repairs, a credit or a price reduction. If your looking at a single family home, I would always recommend a home inspection and a mold inspection. The home inspection will give you a general understanding of the roof, foundation, plumbing, electrical, appliances, HVAC, fireplace, etc. The mold inspection focuses on water/mold issues. So many buyers don’t do a mold inspection, but it’s so important. Water is absolutely damaging to a home and so many times there can be leaks or mold problems that the homeowner is not even aware of. Needless to say, I have all my buyers do a mold inspection. And depending on the age of the home and the existence of large trees on the property, I also suggest a video sewer line inspection which will let you know if there are any obstructions (such as tree roots) or clogging issues. Replacing a sewer line can be expensive and it’s a good idea to know up front what you’re dealing with.