This is a special category as these aircraft are under construction for a number of years, being put together by one or more builders/owners. During this time the chance that damage occurs due to human error (e.g. dropping tools) is somewhat larger than when the aircraft is completed and sits comfortably in its own hanger.
For this and other risks like damage, theft or even fire you will need a special aircraft builders insurance. Aviation insurance companies should have these products available for you.
When building experimental aircraft for a living (manufacturing) you will need a different type of policy as this is a commercial enterprise and the risks are totally different compared to building at home.
Aircraft construction can require special tooling and or jigs, and some of these can be expensive. Tools can be insured as long as you can show a proof of purchase or ownership, so save all those receipts!
It might be an advantage if you record your work time on your kit. Some insurance companies have a reconstruction endorsement that will pay you a certain fee per hour should you need to rebuild your aircraft (or parts of it) after damage.
An important thing to remember is that the value of the kit will increase during construction. Items are constantly being added, avionics, strobe lights, engine(s) and a propeller. Before the annual policy renewal, it is wise to re-evaluate the actual value and have your policy amended if needed.
While under transport from the aircraft manufacturer to the place of construction, the kit should be insured separately. Talk to the manufacturer or shipper about their conditions and possibilities. This is normally not part of the builders insurance.
If you install a totally different engine (firewall forward package) than the kit manufacturer recommends (after all, it is an experimental) then some companies will insure it only after a certain amount of flight time is obtained.
Make sure that you inform the insurance company when you are ready for taxi and the first flight, as this is usually not part of a builders insurance. Any qualified pilot whom is going to fly the aircraft must also be named on the policy (approved pilot status). CFI's might have their own insurance policies.
Basically any pilot can fly the aircraft as long as one of the named pilots accompanies them on the flight.
Normally there would be no policy against landing on grass runways as long the airport is approved by the aviation authorities.
You should consider the risk of such an airport compared to the type of aircraft you fly. E.g. a high performance Lancair is usually more at home with sealed runways than at short backcountry airports.
After you sell your aircraft and if anything happens with it, some will try to hold you liable for any damages. Talk with your insurer if they offer a liability protection and if any, what its conditions are.