No.

When Solomon made God a temple, God said he had put his name there forever. He said his eyes and heart would always be there. Even before the temple was built, God had already decided that he would live in Jerusalem forever, and wouldn’t need a mobile tabernacle anymore.

Yes.

But God also told Solomon he would reject that temple if any of Solomon’s descendants ever failed to obey God. So there was pretty much no chance that he was actually going to be loyal to his temple forever. The only way that could happen would be if every single person who was descended from Solomon always obeyed God perfectly, forever.

By the time of Josiah, God had indeed decided to reject the temple where he had promised to stay forever. And after that, God told Ezekiel that the things his people were doing were going to drive him far from his sanctuary.

Sort of?

After Solomon’s temple was destroyed and before the new one was built, God showed Ezekiel a vision of a temple, and told him he would live there forever. God had already intentionally let Israel’s enemies burn down the original temple, though.