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The IPFS daemon installation will result in an internet facing service being installed. It's not "web accessible" but accessible using the protocols that IPFS uses. Other nodes will contact your instance and communicate with it.

Your node will share its external IP address, and all internal IP addresses configured on the machine it is running with all other IPFS nodes.

You can remove the content after publishing but then other nodes won't be able to retrieve it. If you know the other party has received the content you can use IPFS commands to remove it and eventually, as nodes garbage collect their content, it will go away. This assumes no other node decides to permanently pin your content before your remove it.

You have to have the daemon running for as long as required for other parties to retrieve the content. If you can get another node to 'pin' the content you can shut your node down when that node has retrieved the data.

You are not anonymous. If you share the hash of the content then any IPFS user can go from that hash, to your node hash and from there to all IP addresses configured on your machine with a couple of IPFS commands for as long as you have the content share by your IPFS daemon.