Sure! Here are the rewritten sentences based on reported speech changes:
Ian said that he had been at the gym the day before.
Sue told me that she wanted to go to the park that night.
Brian said that he would help me the following week.
I told Sally that they had met two years ago.
For the reported questions:
"What are you gossiping about?" the teacher asked her students. (This is reporting a wh-question because it starts with "what.")
"Did you see Hello! magazine last week?" Judy asked her friends. (This is reporting a yes/no question because it can be answered with "yes" or "no.")
"Who started these rumours about me?" wondered Tim. (This is also a wh-question, as it starts with "who.")
"Does anyone know when the royal wedding is?" asked Mark. (This is a yes/no question about knowledge and context, although it includes a wh-element "when," it is primarily a yes/no question.)
Now, let's rewrite those questions in reported speech:
The teacher asked her students what they were gossiping about.
Judy asked her friends if they had seen Hello! magazine the previous week.
Tim wondered who had started those rumours about him.
Mark asked if anyone knew when the royal wedding was.