What is ideal temperature for baking cupcakes?

EDITED: Yes, the original old-fashioned pound cake was named that because it used 1 pound each of butter, flour and sugar. Yes, the ratio was 1:1 of flour and butter but it was done by weight, not by volume which is what is in the recipe the op gave. One pound of flour can vary between 3-4 cups, depending on the type of flour (cake vs high-gluten) and how humid it is. And of course a recipe for pound cake (or anything similar) uses eggs that are vigorously beaten to maintain a solid form when baked.

So I stick with what I say about proportion of flour to butter despite what @rumtscho wrote in his comment.

I don't guess that the recipe might be off, I know it is! If you check the recipe @Jolenealaska linked to, the proportion of flour to fat (oil in this case) is 3:1. In your recipe, it's 1:1 - 3 times as much fat. That's more like a brownie recipe but without anything like eggs to bind the mixture, plus yours has the addition of milk. Many brownies aren't that rich as well; neither are brownies expected to rise and have a cupcake like texture.

Best toss out that recipe or recheck the ingredients ratios.

I would say that the eggless recipe is at fault here. It is not a recipe which replaces the eggs somehow, it is a recipe which simply leaves out the eggs. The symptoms are very typical for that case: there is no binder in the recipe, so all the gas created by the baking powder (that first rise you observe) just goes into the atmosphere, leaving you with warm pudding (the sticky mess you observed).

So, if you want a classic cake texture, use a standard recipe with eggs. If you absolutely can have no eggs at all, try a recipe that uses a commercial egg replacer. In the worst case, use some of the homemade replacers, but the texture won't be as nice. As for just leaving out all eggs, there are cakes which do it, but you have to get accustomed to liking the end result.

As the solution here is to choose a different recipe, just use the temperature suggested by your new recipe.

The most common reason for cupcakes to sink is an oven temperature that is too high. 180C is equivalent to 356F. Most recipes in the US for cupcakes call for an oven temperature of 350F. 180 and 350 are just round numbers signifying a moderate oven. Cupcakes are picky though, a very slight difference in temperature can make a big difference in the final cupcake. So try dropping your temperature a bit, and be sure to use an oven thermometer.

Opening the door during baking can cause sinking, so don't do that! (I see that you didn't, so that's one possibility down)

Use fresh baking powder. Baking powder that has been opened for just a matter of a few months starts losing effectiveness. Baking soda on the other hand, lasts pretty much forever if stored properly.

Are you by any chance using Dutch processed cocoa? If so, try adding a small amount (a quarter teaspoon or so) of white vinegar. Baking soda needs acid to work properly, and Dutch processed cocoa has been made nonacidic. Since your recipe also includes baking powder, that is unlikely to be the problem unless your baking powder is stale.

Finally, follow the recipe carefully regarding beating. Overbeating the batter can cause sinking.

That's the best answer I can give based on your limited information. We can help you narrow it down further if you give us every little bit of information you can.