Can I move furniture from one house to another house?

You can.

If you go to the home section you can choose to move furniture, trees etc. Rather than move it, click to add it to the inventory.

Then go to the house you want, again go to the buy home Items section, and select Inventory from the list.

Any Items you have added can go here. It's much better to add older items here rather than sell them, as you can simply add them to other Houses you build.

Yes. You can also move landscaping Objects and Hobby Items. (For example I just bought one Telescope that I move back and forth between scientists.)

Yes you can. Just go to the decorating mode, click on the furniture you want and you can store it in your bag. Then you go to the house you want and click on the bag icon/ storage and you can take it out and put it in the house you want

Only go to the finishing mode, click on the furniture you need and you can store it in your pack. At that point you go to the house you need and click on the pack symbol/ capacity and you can take it out and place it in the house you need