"I have a snake at my house."
Translation:У меня дома есть змея.
I think it's implied by меня and дома following у, notice both are in the genitive case. It's combining two things we already learned: у меня есть = I have, and у дома = at home. If it wasn't "my home" but "your home", or if someone else had a snake in my home, the sentence structure would be quite different.
If that is correct, then it should likewise be possible to say e.g. У него дома есть змея = He has a snake at his house.
My understanding (someone correct me if I'm wrong) is that "дома" carries the connotation of "at home" (which is what we want with this sentence), whereas "в доме" is more "in the house" or "in the building." Not completely wrong (you'd probably be understood) but idiomatically slightly different.
How would I say, "I have a snake house" ? I have a couple of friends who have snakes as pets and I would think of the snake's terrarium as having a snake house in it if there's a covered area for the snake to hang out. I thought this exercise was saying "I have a snake house" rather than "I have a snake in/at my house," so I'm a bit confused.
It seems like the word order is just different, which is normal in Russian. Changing word order usually emphasizes certain parts of a sentence in Russian. As for your question, "есть" means "am/is/are", but it is often seen used with "у + (pro)noun in genitive", which means that said (pro)noun has something. "У меня есть змея" means "I have a snake", literally "By me is snake". Also, "есть" can often be omitted.
We sometimes omit it in the present tense when the existence is not the message or was previously known. У меня дома змея may be more like "There's a snake in my home" or an answer to a question like "Which animals do you have?" (i.e., it is assumed you have some).
Fortunately, in the past and in the future you always use был (была, было, были) and будет (будут etc.) regadless of these shades of meaning:
- У меня был телевизор.
- У меня были кошки.
- У меня будет стол.
- У меня будет кошка.
- У меня будут собаки.