There are not deductible amounts for liability claims that are made against your insurance policy. The third party claim made against your property damage liability coverage does not come with a deductible for you or the person making the claim.
If you make a claim for any damages your car sustained in the accident through your physical damage collision coverage then you would have to pay the deductible associated with this coverage. The amount of the deductible would be listed on your policy as you chose it at the inception of your auto insurance policy.
As for the surcharge, since you were at fault in an accident it is likely that a surcharge might be applied by your insurance company. The amount of the surcharge and length of time that it will affect your insurance rates will differ depending upon what state laws allow and then the guidelines and rating system of your insurance company.
In most states the insurance laws and regulations allow an insurance company to determine their own rating systems and surcharges. Typically however surcharges last 3 years but can last longer such as 5 or 7 years. There are states like Massachusetts where the state sets up the rates and surcharge system. Here the state has determined what incidents are surchargeable, the points associated then with the incident and how long the surcharge will last.
In MA even if your driving record contains surcharge points, the system has built-in incentives for improving your driving. If you have no more than 3 surchargeable incidents over the last 5 years, the point value of each of those incidents will go down by 1 when you have 3 years of incident free driving.
Your agent should be able to give you more information on your insurance company's rating system and your state's insurance regulator can give you information on state insurance laws and regulations regarding surcharges.