What do these mean here?
1. What does 'wine and dine' mean ?

The firms spend millions of dollars love-bombing these institutions with recruiting events: students can spend the recruitment season wining and dining at their expense.

2. Does 'game the system' here mean 'how to get selected' ?

However, as Ms Rivera notes, firms reject the vast majority of elite students they interview: so even the most pedigreed need to learn how to game the system.

3. Does 'learning the ropes in boot camps' mean 'to learn how to face/manage a difficult situation' ?

They also expect their employees to spend extraordinary amounts of time together—learning the ropes in boot camps, working late in the office, having constant work dinners, getting stuck together in airports in godforsaken places.

4. Does 'go to bat' here mean 'to recommend' ?

The final key to success is to turn your interviewer into a champion: someone who is willing to go to bat for you when the hiring committee meets to whittle down the list.

Thanks.http://www.economist.com/news/business/21651207-book-persistence-elites-unexpected-guide-getting-good-job-how-join

Question

What do these mean here?
1. What does 'wine and dine' mean ?

The firms spend millions of dollars love-bombing these institutions with recruiting events: students can spend the recruitment season wining and dining at their expense.

2. Does 'game the system' here mean 'how to get selected' ?

However, as Ms Rivera notes, firms reject the vast majority of elite students they interview: so even the most pedigreed need to learn how to game the system.

3. Does 'learning the ropes in boot camps' mean 'to learn how to face/manage a difficult situation' ?

They also expect their employees to spend extraordinary amounts of time together—learning the ropes in boot camps, working late in the office, having constant work dinners, getting stuck together in airports in godforsaken places.

4. Does 'go to bat' here mean 'to recommend' ?

The final key to success is to turn your interviewer into a champion: someone who is willing to go to bat for you when the hiring committee meets to whittle down the list.

Thanks.http://www.economist.com/news/business/21651207-book-persistence-elites-unexpected-guide-getting-good-job-how-join

Answer

1) Wine and dine=eating and drinking, usually lavishly
2)Game the system usually means to make it work; in this case however it means how to know the tricks of interviewing and how to get selected.
3)Learning the ropes in boot camps= learn the ways of the work/lessons and the style of them
4) Go to bat= do it, in this case it means to stand in place of you and yes, you are right, to recommend.
Hope this helps!