Explanation

Box 1: Yes
Code for CosmosDB, example:
// Parse the connection string and return a reference to the storage account.
CloudStorageAccount storageAccount = CloudStorageAccount.Parse(
CloudConfigurationManager.GetSetting("StorageConnectionString"));
// Create the table client.
CloudTableClient tableClient = storageAccount.CreateCloudTableClient();
// Retrieve a reference to the table.
CloudTable table = tableClient.GetTableReference("people");
// Create the TableOperation object that inserts the customer entity.
TableOperation insertOperation = TableOperation.Insert(customer1);
Box 2: No
A new record will always be added as TableOperation.Insert is used, instead of TableOperation.InsertOrReplace.
Box 3: No
No partition key is used.
Box 4: Yes
References:
https://docs.microsoft.com/en-us/azure/cosmos-db/table-storage-how-to-use-dotnet