- In daily conversation, " 雷 " means both the lightning and the accompanying thunder as a single phenomenon, right?
- At night, I sometimes see lightning on the horizon, but no thunder. That is 雷, right?
- All the time, I hear the thunder, but not see the lightning. That is also 雷, right?
- Does "雷を見えた？" sound like natural Japanese?
- Does "雷を聞こえた？" sound like natural Japanese?
Yes, 雷 refers to both the lightning and the sound caused by it.
If you need to distinguish, the specific term for the visible discharge of the light is 稲妻【いなずま】, and the specific word for the sound is 雷鳴【らいめい】. Although these words often appear in news media and scientific papers, we usually just use 雷 in everyday conversations.
As for the last two questions, the natural ways to say them are "雷(が)聞こえた?" and "雷(が)見えた?". "が" is often omitted in conversations, and we don't use "を" there.
雷 refers to both lightning and thunder, though tends to suggest lightning more than thunder if you use it on its own (this would be the image that comes to mind when you say it). 見る, 聞こえる are both valid to use, but should take が and not を, because they're sensory. You can hear a dog (bark), so why wouldn't you be able to hear lightning (crash)?
Your two sentences are both valid, but should read in the general form as:
For all extensive purposes, the everyday use of 雷 is for lightning and thunder, and context reveals which it translates better into English as.
And finally, something from the comments that's worth clearing up:
電 now refers to electricity, not lightning. It meant lightning in the past, perhaps, though now is definitely electricity, and not lightning.