An excavator is a very specialized tool that does a couple of things really really good, but it's also horrible at just about everything else. Transporting stuff, or moving anything is one of those things it's horrible at.
On your list, an excavator is probably the best tool out there for stump removal. Digging is what it excels at. The more HP, the better it is. Just remember that not all stumps are the same, some trees have shallow roots that are easy to take out, others have deep tap roots that can be very difficult to take out.
Drainage ditch maintenance is the only other thing on your list that the excavator might do well. It might also be very time consuming and not the right tool at all.
For transporting logs, you want something on wheels with a grapple. Tracks are very slow.
Road maintenance can be one of the most frustrating things you will ever do. The blade on a mini excavator is for short distances, small piles of dirt. But mostly it's to stabilize the exactor while digging because it's so light and unstable. Trying to use it for dozer work will be very frustrating. I personally like to use the loader bucket for maintaining my roads. I can carry a load of dirt or gravel to where I need to fix my road, dump it, spread it and smooth it out with the front bucket faster then I can with anything else.
While an excavator with a thumb is capable of lifting things overhead, I believe that the front end loader on a tractor is much more practical and easier to use. You can remove the bucket, use pallet forks, or a grapple, or even attach a boom to the loader for lifting things a lot higher, like setting trusses if the tractor is big enough.
An excavator does do a good job at feeding a burn pile, but it's so slow that this is why so many excavators catch on fire. Once you get too close to the fire, a hose melts and hydraulic fluid sprays out. The fluid is very flammable and when this happens, there isn't any hope to save the excavator. It's good for picking up branches to build he pile higher, but a burn pile shouldn't be too high. Long and thin is best so you can control the fire. Once the fire is going, a tractor with a loader works treat at punching up the fire to keep it going. Those bigger logs don't burn very well, so they need to be moved around to keep the fire going. You want to push them, back up quickly, change position, and do it again and again. I work my way around the entire burn pile several times pushing everything on top of itself with my tractor until there isn't anything left.
In my opinion, a Loader Backhoe with a quick attach front bucket and the hydraulics to operate a grapple is the best machine to do everything on your list. It's not the best at digging up stumps, but if gets the job done. And once the stump is out, it's better then an excavator at filling up the hole by being able to haul dirt to the hole, fill it up, compact it and smooth it out. Where you spend you money on a backhoe is in HP, cab or open station, 4x4 and how new it is. A 20 year old Backhoe works just a good as a brand new one, it's just not as fancy and you have to wrench on it more often. But if the HP is the same, an older one will do what a new one will for a fraction of the cost. I paid $18,000 for my open station, 2wd 555E backhoe 20 years ago, and it's still running strong. I've taken out tens of thousands of trees with it, and moved thousands of yards of dirt with it. I plan on doing more this year and every year in the future. My neighbor hires guys with excavators to work his land, then somebody else with a dozer, dump trucks and loaders to clean up the mess. I do it all with my backhoe for a lot less money, but I spend a lot more time doing it myself on one machine then he does paying to have it done.
When my backhoe finally dies it's final death, I will buy another backhoe. I'll get 4x4 next time. More traction would allow me to get even more done, even faster!!!
