I'll only try to answer your last 3 questions, because I don't know for sure how your first question works (to avoid misconceptions).
2. Can the token sky rocket its price after getting listed KNOWING that the game is far from the release?
Yes, it can. But you need to know that this price increase will not be completely driven by the community or potential adopters but rather the price will be increased by the project team itself.
3. Should I expect a 'dump' after the token launch because the majority of the investors who bought in pre-sales are talking about making quick gains when the token launches next week.
You should expect that, just like the airdrop, the tokens from the pre-sale will also be immediately sold by those who bought. Yes, at least they want ROI or 2x first.
Note: for projects that have a lot of attention and good fundamentals, the decline in token prices will not last long.
4. (For the experieced investors): When should be the best time to buy this token? After the game's release OR when the release time approaches and as how the hype gets build up by influencers?
It depends on what type you are, if you can accept more risk, it's better to buy it when the release time gets closer. And if you're the type who usually plays it safe, buy when you know what the final product is like.