what did Japan do to Korea during its annexation

They took over all of Korea and made it a part of the Japanese empire. During their time in Korea, they:

• built an information network consisting of police and local informants to keep tabs on everyone (where do you think North Korea got the idea from?)
• during the first part of the annexation, they dealt with Koreans very directly and harshly. Around the 1920's, they began to take a more hands off approach and used their information and control to direct Korean independence energy where they wanted it to go, usually nowhere.
• they built shinto shrines all over the country
• they required all Koreans who wanted to work in the government or go to school to adopt Japanese names. Near the end (1940s), they required ALL Koreans to adopt Japanese names.
• during the war, they lured young Korean women into prostitution, using the prospect of good factory jobs as bait.

Long story short, they did a lot of really shitty things.

But on WIkipedia, there's a list of apologies Japan made. Are they not considered real apologies?

No, they aren't.

There are a few issues. First, the Japanese apologies frequently use language that is indirect. They don't simply say "we're sorry for what we did," but they "express regret for what happened." Second, and much more importantly, there are three audiences: domestic, international, and Korean/Chinese (China is just as much a victim as Korea is). While international audiences (Europeans, Americans, YOU) see the apologies that the Japanese have made and think, "what's the problem, they've apologized, move on!," the domestic (Japanese) audience sees "we've lost face, we've shown we are weak" and then the right-wing politicians get antsy and issue denials or retractions or clarifications. So what the third audience (Koreans) sees is Japan apologizes on the first day with a lukewarm apology and then the prime minister takes his colleagues to the Yasakuni Shrine and then issues a statement "clarifying" the apology.

Really, without breaking the 20 year rule, it's pretty tough to discuss here because the first major apologies came out during the mid 90's, and then a lot of the trouble has come from Shinzo Abe and his party, who are in power now. I'd suggest reading the Hankyoreh (left wing paper) and the Joongang Ilbo (center-right wing paper) and search for articles on Japanese apologies. There was a big one in December of 2015 that was supposed to be a huge breakthrough and then within a few days it became a huge controversy.

how do younger Koreans (teens-20s) feel about Japan?

Again, 20 year rule and anecdote rule, but if you look around for surveys, you'll find some information.