Which technology can I use to securely store private keys associated with our internal accounts?
There are multiple different options for storing your private keys, each with its own set of pros and cons that you will have to use in order to decide which one is best for you. You could use a cold wallet such as Trezor or Ledger. Or you could keep them on a hard drive/computer that isn't connected to the internet.
What's the recommended tool or method for deploying smart contracts using our own wallet addresses?
There are also a handful of different tools you can use to deploy smart contracts. Three popular ones are Truffle, Hardhat, and Foundry.
How should I facilitate interactions with the smart contract, especially by the contract owner and our internal accounts?
You can interact with your contracts directly from an EOA, you could call your contracts from another contract, (which would initially need to be interacted with by an EOA), you could write scripts to make function calls in Javascript or Python, or you could even make a frontend/UI to interact with the contracts. Regardless of the method, you will need an Ethereum account.
Which solutions are best for capturing notifications and blockchain events in real-time?
Like most of your questions, this one has multiple answers. To say who is the "best" is in the eye of the beholder, but you could use a tool such as QuickNodes or Near, or write your own listener with something like ethers.js. Here and here are some guides on this topic.
What approach should I adopt for executing scheduled operations on smart contracts?
One approach you could take would be to use Chainlink Automation. This allows you to set either a time interval or a logic-based trigger, that will call your contract whenever the condition is met.
