Correct. 더 can be omitted in this case but only because 훨씬 (더) is used with an adjective, 크다.
It can also be dropped from 훨씬 (더) when used with an adverb.
• 훨씬 (더) 이상 말할 수 없다 - cannot say much more [이상, more than - adv. so either 훨씬 or 더 can be used as intensifier]
• 훨씬 더 먹었다 - ate much more. [더 cannot be omitted in this case]
So in superlative, is the house being compared with the other houses or the previous unrenovated house? And for the comparative and the example question, the house is being compared with the previous time of the house ? (I mean the house before this bigger renovated house)
Apologies for having explained badly. The 'renovated' house was just an example. Basically,
• A Superlative is used in a sentence where an object ("저의 집, my house in this case) is compared to a group of objects (other houses in the street, for example)
It is an adjective which describes this object ("저의 집, my house) as being at the upper or lower limit of a quality (the -est, e.g. the biggest).
My house is the biggest by far -> no other houses (in the comparison) can be any bigger.
• A Comparative adjective is used to compare the difference between an object with another object. (- er than/more than e.g. bigger than).
My house is so much bigger -> bigger than another house (which could be my house pre-renovation, for example).
Hope I am not confusing you further.
"House" (= 집), if you are talking about the building itself.
"Home" (= 가정), if you are talking about the familiar space where you and/or your family live in. There is a certain amount of personal emotion attached to this word.
"Home" is also used sometimes to refer to one's family.
집은 크지 않지만 저의 가정입니다 = The house is not big, but it is my home.