We have had an I3100 for a couple of years now and really like it.
First off just to clarify a little, the I3100 and HI300 are a little different, the I3100 has a 2.9cuft firebox, the HI300 is 2.3. That 1/2 cuft makes a big difference in this case (our Nap stove has 2.25 cuft and can't come close to the perf of the I3100.)
1. For starting we now use the Pine Mountain starter "log" firestarters. They're kind of a brick thing. We break one in half, throw a couple of splits on the bottom, the 1/2 brick and a couple of splits over top of the brick. Open the air full, close the door tight and 1/2 later, fire is going well. This is the only way my wife will start a cold fire. No smoke, no fuss. Have you checked your door seal and gasket? Try the dollar bill test to make sure you don't have a little seapage into the room. Also as someone else mentioned, make sure you have no stove or bathroom fans running when you're starting a new fire, this will draw smoke back into the room in most cases. Plus there's no dinking around with an open door (dangerous) or fussing with it. Those starter logs come in boxes of 24, so using 1/2 at a time gives us 48 cold starts, usually way more then we need in a season. Last year we started once in Dec and didn't use another until end of Feb. For re-loads, I turn off the blower and rarely get much smoke back into the room. As soon as I close the door, blower goes back on.
2. Operating the I3100 is pretty simple, but can be a little tricky. You may not be letting it get hot enough to burn efficiently (presuming you now have some decent dry wood). The thermometer will help. We have ours just above the LHS corner of the door on the front face. I also have a cheap IR gun which I use more to check the magnetic than anything. I let it get up to between 500 on the front of the stove (which is a little cooler than the actualy stove top temp becuase of the way the insert is "wrapped" in steel. Once it gets up to that temp, we shut down 1/2 way for a few minutes, then all the way down. With that we get nice secondaries and the stove temps usually go up some as the stove gets hotter from the sec burn. When we started I had similar issues and my installer suggested getting it to the temps I mentioned. It worked much better even with somewhat "wetter" wood. I leave the blower on low speed all the time (except in the early fall/late spring) and it pushes out enormous amounts of heat.
3. In your area you should be getting a decent mix of hardwood - it all burns great. If you have lots of Oak, split it small and let it season for 2 years if you can.
4. "Burn time" seems to have the ad hoc definition of something like "amount of time between loading the stove to the gills and when you can put in more wood without having to re-start from scratch"

Truth be told, for the nights, I fill it up N/W as much as I reasonably can and usually 8 hours later when I get up, I simply throw a couple of splits on in the morning and open the air full. If it's really cold, I'll fill it up in the morning and it catches pretty well. If you're only getting 3-4 hours, either you're not filling it up enough, maybe turning down too late, not turning down enough, maybe not getting hot enuf to turn down fully, some combination of the above.
5. We use a single 12" floor fan to circulate air in our 1800 sqft bungalow - 1/2 open concept. Our bedroom was 78F last night when we went to bed - O/S temp was 28F. I tried using my central blower and it really wasn't that effective, plus it's a much more expensive fan to operate. If it works for you, great - try a smaller fan blowing in to the stove room for fun just to see if it works and you may be able to leave the furnace fan off.
I'd suspect that you have a combination of a) some wood that is less than seasoned and b) need a little adjustment to your technique (temp b4 turn down etc). Once you get it dialed in you'll be toasty warm I'm sure.