e. I (walked) for half an hour when it suddenly started to rain.
(The sentence is in past tense, so the verb needs to match this).
f. I don't fancy (going) out tonight. It's too cold outside.
(I'm honestly not sure about the explanation for this one, but I'm a native English speaker and this sounds right).
g. We are leaving on Wednesday or not it rains. (whether)
(In no case will you use "if" and "or" right after one another in a sentence. "Though" would also not fit into this sentence.)
h. I talked to the girl hocar had broken down in front of the shop (and) he (asked me how much money I had.)
(I don't know quite what's being asked with the first part of this question. However, indirect speech would turn a direct quote into a summarization of what someone said).