New construction vs. existing home are different. There is no contingency for inspections per se, but there is a contract with the builder that includes certain requirements. They have to meet code, have to provide the finishes contracted, etc. There is typically a pre dry wall inspection to review before they close up, a coming up on settlement inspection, a pre settlement day of/before inspection, and a 1 year warranty. If you are not versed in construction it is advisable to bring an expert to represent you in reviewing the work. Things that look terrible are often not, and things that look fine are often incorrect.
Real Estate is very State specific, which is why people recommend a lawyer if you are worried. When I signed my contract in VA I had to provide a 20% down payment within a week of signing. If I did not meet my obligation under the contract I would forfeit the down payment. They also have obligations, but the contract is written to favor them. For ex. they promise a 4 month delivery, but if you read the contingencies in the contract they can actually be a year+ late without violating their contract. Reality is that well known builders want to sell houses and the cost of repairs are usually on their subcontractors so they can be your advocate to make sure the work is done correctly. A nice 6 pack to the site foreman can go a long way
If things blow up then your money is going to be tied up for a long time until the arbitrator or courts decide if the contract terms are enforceable or who was at fault.
For your agent, if they have a broker, you need to complain to the broker and get a resolution. No agent should be paid for doing nothing. Even in new construction they should be guiding you through the process. If your agent is the broker then you need to complain to the state board that licenses the broker. That behavior is not acceptable.
My guess is that you will be fine if you can get an experienced person to help you navigate the process. Thousands of homes have been built and it is a known process. That is what the agent should have done and I am sorry that they failed in their responsibility.