Volume of a 10" cake pan will vary with the wall height (which varies by manufacturer). The 11 cup measure is for a 2" tall pan; if it calls for a taller pan, you might have issues.
As for how to deal with preparing the pan as you can't use parchment would be to butter and flour it; it generally works better than most cooking sprays. If you use a cooking spray, look for a baking specific one -- they have flour in them, so it behaves more like a floured pan when releasing.
You can also make 'cake release', which is a blend of shortening, oil and flour (equal parts by volume) that you can paint onto the nooks and crannies of pans with a pastry brush.
As for the cooking temperature, I would shorten the time before I started checking for it to be done, but I don't know that I would drop the temperature; when you do, you end up with less doming but a denser cake.
As the commenters have already said, it's hard to know exactly what happened from the information you've given but I'm going to try to give some direction.
First, I think the key is in this statement:
"the pastry was not all well creamed and looked oily as I placed in oven".
This sounds like either the oil (butter, in this case) separated out from the batter, or it wasn't well-mixed to begin with. Let's assume that you mixed it thoroughly to begin with until it seemed like a creamy, smooth batter and everything seemed well-incorporated.
So, what happened? I'm guessing that you left the eclairs-to-be resting on the pans for a while, maybe while you were piping out the rest of them.
If you let the batter sit for a while, oil can start to separate out, especially if your kitchen is pretty warm (which they can be, in summer when boiling water on the stove and pre-heating the oven). This shouldn't happen immediately, but I think it would explain what happened.
Next time, make sure everything is ready and laid out before you start. Start to pre-heat the oven before you start boiling the water. Once you start piping, move quickly, and if possible, work in a cooler part of the kitchen. Pop the trays directly into the oven as soon as you finish piping them all out.
There's a second thing you said that I think is significant. You said that the outside was rock-hard but the inside was too moist. I think the excess moisture is from steam.
It is normal for the eclair to have a bit of a crust to it (not rock-hard, of course, but there will be a crust) and this traps steam inside. You need to break a hole through the crust to let the steam out, and my guess is that either you may have missed this step, or the hole you made wasn't big enough.
BTW, it is also possible to have something get too hard and still be raw in the middle if you cook for too long at too low a temperature (it dries out instead of cooking) but you said you cooked for 30 minutes and that matches the recipe timing, so I don't think that was your problem here. But if you have a lot of problems with things not taking the right amount of time when you bake, you might want to invest in an oven thermometer and see if your oven is heating to the temperatures you expect. Not all recipes are very finicky about exact temperatures but some are.
Best Answer
Batters full of starches and sugars are always sticky, how you prevent it from sticking partly depends on the plan. Some pans have coatings which while called non-stick aren't, but do reduce sticking somewhat. On pans like these often buttering is sufficient, and 'normal' cake pan shapes allow you to loosen the sides by running a knife around the side, so even if they stick you can free the cake. Putting a piece of baking paper on the bottom of a flat bottomed pan is a sure-fire way of preventing issues.
When you have an odd shape like a bundt, paper won't work, and you can't afford anything sticking, so the best way to ensure it frees is to generously butter (not oil or spray) the pan and then flour it. You can also make cake release, which can be sprayed or brushed on, using equal volumes of flour, oil and shortening.