cake baking problem (white lumps of flour)

How it's supposed to be done

The lump problem is straightforward: your mixing technique is failing.

When you are using a well, you have to sift the flour first. Then you add a little bit of the homogenous liquid. So, you don't pour oil, eggs, etc. into the well, but first get them all into another bowl (including the water), and mix them well, preferably with an electric mixer, until they are very homogenous. Ideally, the eggs will emulsify the oil a bit.

For the actual ingredients mixing, you now pour just a little bit of your eggy mixture into the well, maybe 50 ml. Then you take a spoon or other utensil and start stirring the egg mixture without touching the flour with the spoon. A little bit of flour from the walls of the well will stick to the liquid surface and start sinking in, thickening the liquid. Once it is noticeably thicker than the pure mixture, you add some more of the egg mixture to thin it back, then continue back and forth, thickening the batter with the flour then thinning it, until you are done.

When you feel more comfortable and know well how the flour and liquid acts, you can start carefully spreading some flour from the far side of the flour "volcano hill" (not the well edge) onto the liquid, to get it a bit quicker. But in general, it is a finely tuned skill which you have to learn from experience, by doing it slowly and with concentration. If you impatiently stir too much flour into the liquid, it forms the lumps you described.

A more sensible alternative

This is how to execute the recipe correctly. It is a good, but very long method for even mixing. But frankly, there is no need to use it. Nowadays we have electric mixers, which will mix the flour for you into the liquid ingredients without creating lumps. And we have scales, so we can weigh the ingredients. So the second advantage of the well method - you stop mixing the moment the batter has the right consistency (which is necessary when you cannot measure the flour, or don't have a written recipe and are playing it by feeling) - is also moot. If you don't want to spend half an hour mixing your cake batter by your grandma's way, just emulsify the liquid ingredients with the mixer, then slowly add the sifted flour with the mixer turned on on low speed, and stop the moment it's mixed in. That's it.

Water temperature and boiling

As for the water, I see no good reason to boil it from a food science point of view. All the explanations I can think of make it seem unnecessary.

• The recipe is so old, it comes from a time with bad water supply. The water was always boiled for safety and to precipitate scale, rust and other stuff present. Shouldn't be a concern today. (If your water is very hard, filter it instead).
• The eggs and oil are meant to emulsify, to give you a smoother mouthfeel in the cake. It is like making mayonnaise, and works best when the eggs are warm - but fails completely when you make them so hot that they curdle. 72 Celsius would be optimal, but anything between 60 and 83 Celsius should work. If your water is warmer than that, it will curdle your eggs, doing more damage than good. So, if you are pouring the water in just after boiling, stop doing it (although it doesn't cause the lumps you described, it causes cruder texture overall). The best thing would be to warm it to 80 Celsius using a thermometer, then pour it into the eggs, beat, then add the oil. If you don't have a thermometer, take it off the heat the moment you see the first tiny bubble forming on the bottom, then let it cool for a minute before pouring.
• The soda dissolves quicker in warm water. This is still not a reason to get it to a full boil - take it again to 80 Celisius, instead of boiling first and cooling it afterwards.
• The whole ingredients are too cold when coming directly from the fridge, and the hot water is supposed to correct that. But in fact, this won't work well. Temperature shocks are not good for cake ingredients, especially for eggs. You should use room temperature eggs and buttermilk instead.

The boiling water is actually an integral part of the recipe - the heat insures that the cocoa powder fully dissolves and contributes to a richer, more chocolate-y cake - and adding the baking soda to the water first will probably have more to do with enriching the color of the final baked cake than it has to do with leavening. It is NOT tied to sanitation issues. Please do not neglect this part in your process!

Also, you need to be a little careful about the order in which you add your ingredients - for instance, you can't just mix-up your eggs in the boiling water because that would cook the eggs - the eggs need to go into the batter when the batter is cool enough to prevent coagulation.

I assume that what you are making is a good old-fashioned chocolate cake using cocoa. Here's a link to a recipe from Hershey's - I know that you want to perfect your family recipe so I'm not trying to suggest you abandon your link to the past - I include it here because you might find the directions (and the order of operations) helpful if you apply them to your cake.

https://www.hersheys.com/recipes/recipe-details.aspx?id=184&name=HERSHEY%27S-PERFECTLY-CHOCOLATE-Chocolate-Cake