Hi! Why did my cake turn out so dense?? and a question.

Sorry in advance if I'm breaking any rules!

Okay, so I recently made this lemon cake but it turned out pretty dense. I followed the recipe to the letter, except I took about 3/8 of the zest and rubbed it in with the sugar(Saw that on an orange cake recipe) and I used the buttermilk substitute of 1/2 cup milk + 1/2 tbsp of lemon juice. but the cake turned out very dense. Is that supposed to happen??

Also, additional question. The glaze at the end that has lemon juice and confectioners sugar, I added a looot more icing sugar till it was about the consistency of diluted honey. So pretty thick but not thick that it wouldnt spill if I knock the bowl over. Anywayy. it tasted rlly good on top of the cake, but what if I put the mixture in the middle of the cake?? Like before baking, if I pour some batter, some mixture, and then some batter?? If not, would it be okay if I make some cuts in the cake and then glaze it to get that sweet/sour taste inside the cake as well??

Thanks in advance! The link for the cakes below if anyone wants to check it out

https://platedcravings.com/moist-lemon-cake-recipe/#wprm-recipe-container-5618