yes it is possible to complete the transaction without an agent but i do recommend closing with a lawyer. You should nto go to closing without the title search already completed. And yes, you can have in the contract that the closing is based on the title search.
Your last steps seem correct but once again I always close with a lawyer. Its the best way to protect your investment - - money well spent.
Is the property listed with an agent? If so then it won’t cost you anything to have an agent represent you. The seller pays the agents commissions.
If you don’t use an agent then find a good title company. The title company will be the ones doing the title search and all the other stuff you mentioned.