1. Topic id is for topic. All forums have topics and each topic has it's id.
Forum id is a forum (sub-forum) where topic is. All those sub-forums also have their own ids.
2. When you enter a forum look in the url address, or just press "New Thread" button and look into url address.
3. p=45455 is post id, not the topic id. You simply have the wrong link, go back to main sub-forum and then enter your topic, you will see t=11111 . Every forum has topic ids and post ids. Those are two different things. When you create new thread you are usually redirected to "post id", not the topic id, but your topic also has the id, it's just wrong link
. That's how most of the forums works.