The last fork didn't changed changed the difficulty for Bitcoin core too much, I don't think the next fork will.
There are several alts with different difficulties, I don't know what will be different with the next fork
I agree with this. I have a feeling that bitcoin gold will go pretty similar to bitcoin cash. Investors of bitcoin will end up dumping the btc gold in order to get more bitcoin with their holdings. Chances are that this will raise price and introduce more investors into the whole bitcoin scene as well.
I don't think that this "new bitcoin" will make the mining easier. As mentioned, the last split didn't have that much impact in the bitcoin mining. And those who have choose to mine BCH earlier moved back to bitcoin mining because there's not much incentive to gain. It will be the same with Bitcoin Gold, those that will support this in the beginning have no choose but to go back to bitcoin mining because it will not gain any traction to the community, which means no profit for them. So I doubt that the difficulties in bitcoin mining will be affected by the next hard fork.