Learn Russian: У нас дома широкий подоконник.

Дома acts as an adverb meaning "at home" or "at one's own place." В доме physically means "inside the house" or "inside the building." Since the speaker is talking about their own living space, дома is the natural choice.

Why is широкий подоконник in the Nominative case? Isn't it the object of "we have"?

In Russian "have" constructions using у нас, the thing you possess is grammatically the subject of the sentence, not the direct object. Because it is the subject, it stays in the Nominative case. Literally, this translates to "By us at home [is] a wide windowsill."

Why is the word есть missing from this "we have" sentence?

While you could say у нас дома есть широкий подоконник, Russians typically drop есть when describing the qualities of an object you have (like it being широкий - wide) rather than simply confirming its existence.

The word подоконник looks long and difficult. Is there an easy way to remember it?

Yes, you can break it down into familiar parts! It is made of the prefix под- (under) and the root for window, окн- (from окно). A подоконник is quite literally the structure "under the window."