the easiest way i found is to put in the beams. Then i put tiles on one side of a beam (no tile on the last one) and put one tile less on the other side of the beam. Repeat until you filled all beams. Thats the easiest why and i looks relativly clean, middle is your chimney ^^.

To cover the middle of chimney the easy way is to put a roundlog at the center point and circle it with the corner pieces. Gives a nice effect and looks relativly nice. But the circular building now looks weird :), looks a little bit like a mushroom growing out of it :D. If the building is high enough in the inside, you can mount the umbrella under the chimney. The umbrella design i used in my Resort build for the you guessed it umbrellas :D. The other roof i used for my Chaos Temple build and for the half round portal hub in the Resort build if you want to see how it looks like.

Alternative to my last response once. For your particular roof I suggest laminating beams of the same angle to the sides of the current beams to close in the gaps. They will act as roofs and keep rain out and even give the sheltered buff. If you look at my Roundhouse portal hub on here you will see this method done

To build a dome you should lay out a circle with beams. Either 1 rotation per piece or 2 depending on the desired size. Then snap roof panels to the circle and work your way around and then do the next layer. A 26 degree roof will have a lower dome than a 45 and you can mix both together for a slightly different dome as well. You should be left with a small circular hole at the top if done correctly. You can cap that off with a 2x2 floor panel or a 1x1 floor panel.

The build tool is very forgiving. So when you build the roof up and it begins to meet and overlap each other it will blend together becoming very smooth if you place the pieces correctly.

That's a challenging roof to cover with current thatching options. I think you did a great job with what you've got available though. Building is solid design, should be "easy" to update.

As you mentioned, hopefully the Hearth and Home update adds both basic building blocks along with whatever they must have planned to dedicate an entire update to. I love that the first major planned update is going to focus on builds.

I really like how the center beams cross together at the very top to make a chimney!