HS TARM SOLO PLUS jacket insulation/repairs

Not usually - it doesn't really get too hot in there!

You could use either rockwool or some particular fiberglass made for relatively high temperatures. I think you can find some of this stuff at drywall supply houses, but you can also see it on McMaster-Carr

example:
http://www.mcmaster.com/#9328k41/=ppyhk9

Most of that boiler is surrounded by water - those surfaces will never pass about 250, but any single wall surfaces (maybe around the flue and cleanout area) could hit as high as 800+ degrees.

The boiler is not designed to be fired up without water in it! Not sure where you came up with that idea, but a boiler like this maintains about a 200 degree temperature in normal use (the steel), while it can be 5X that without the water...or even more.

Firing a boiler without water is like running a car engine without water.

As I remember, that flap was weighted or something like that so it would close when the fan was not running. However, none of these assemblies are really designed to be "smoke tight" to the degree you may be thinking.....so unless your chimney has some kind of a draft, you are going to get smoke.

Also, remember that these boilers are usually used with storage - in most of those cases, the boiler runs the vast majority of the time (or all the time) with the fan on.

The importer should have the new door gaskets as well as the door mounting gaskets.

If the fire is out how can there be any smoke to go anywhere?

It needs to be able to breathe, yes. Personally, I just crack a basement window a tiny bit that happens to be right above the boiler. If your house isn't real tight, you might not have to do anything. Most don't. If you make sure your chimney is solid, and draft is to spec, and there shouldn't be any of the smoke or gas issues you speak of.

Verify your chimney draft is to spec.

I have a recollection that the specs for the Tarm are to use inside, warm air, not cold, outside air.

To insure adequate combustion air, I have a linear actuator attached to a slider window. When the boiler is turned "on," the actuator opens the window 6". When the boiler shuts off, the actuator closes the window. There are website which give info as to how much air vent in sq inches is needed based on the size of the boiler. Because my shop is not airtight, the 6" opening is somewhat less than sq inch need.

I rarely get any smoke roll out, but as others have said, if you let the wood load burn down to low coals before opening the door, you should not have any smoke problem, assuming you then shut off the draft fan, you have adequate chimney draft, fresh air supply, and seasoned wood to start with.

If you mean it actually sounds like it's boiling, or making boiling noises - I don't think that's quite right.

Hope you're keeping a good eye on temps & pressures? The more places the better, especially when you're getting things up & going the first time.