Is my translation correct in the following examples?
If (when) I build a house I will buy furniture.
家を建てたら、家具を買う。
If I built a house I would buy furniture.
家を建てたなら、家具を買った。
If I build a house I will have a place to live.
家を建てると住む場所がある。
If I build a house I will buy good furniture. 家を建てれば、良い家具を買う。
If (when) I build a house I will buy furniture.
家{いえ}を建{た}てたら、家具{かぐ}を買{か}う。
Correct. That is an exemplary use of 「たら」 for a specific and/or one-time-only condition-consequence relationship.
In a real-life setting, however, the 「買う」 ending would sound quite blunt. It would be more natural to say 「買うつもりです」、「買うと思{おも}います」, etc.
If I built a house I would buy furniture.
家を建てたなら、家具を買った。
Ungrammatical and unnatural. Why use the past tense 「買った」 here? You have not bought the furniture yet. Moreover, you have not even built/bought a house yet as you utter this line.
In a proper and natural use of 「なら」, the second half (the consequence part) would express some kind of opinion, judgement, wish, etc. of the speaker. A verb phrase in the simple past tense (as 「家具を買った」) would generally not fit there.
A natural-sounding second half would be along the lines of:
「素敵{すてき}な家具をたくさん買いたいです」,
「イタリアまで家具を買いに行くつもりです」, etc.
If I build a house I will have a place to live.
家を建てると住{す}む場所{ばしょ}がある。
Nice try but sounds unnatural on the native level. When native speakers see/hear the condition 「家を建てると」, we will naturally expect to see/hear that something will happen as a result of it.
The problem here is your verb choice of 「ある」, which is stative. It is too weak to make something sound like an "action". Change it to 「できる」 and it will instantly satisfy the reader/listener's expectation of seeing/hearing about what would happen then.
If I build a house I will buy good furniture.
家を建てれば、良{い}い家具を買う。
Grammatical but unnatural. (Again, I am speaking on the native level because that is the ONLY level on which I can judge these things. For all I know, your sentences might be graded as A+ in a Japanese-as-a-foreign-language class.)
「れば」 should be used to express a constant and/or permanent kind of condition-consequence relationship.
It might certainly be somewhat universal to buy furniture if you build a house, but buying "good" furniture is not, is it? Buying "good" furniture is basically this particular speaker's desire.
As I stated in the beginning, 「たら」 would be a far better and more natural word choice here.
