For partner airlines Flying Blue is part of the Sky Team network, so Flying Blue Gold is the top tier of Sky Team Elite Plus.
That gets you benefits that same as you would with any other Sky Team program membership except perhaps the native program for the airline you fly.
All other things being equal it is usually better to put most of your frequent flyer credit on to the airline you fly most frequently, which it sounds like is Delta for you. But I have no clue about the Delta program so can't comment on that.
On Korean Air Sky Team Elite plus get access to priority seats within their paid cabin from time of booking. But I don't think this applies to other pax on the same booking. You get one guest to the lounge, not the whole party. The group will usually all be able to use the same checkin desk.
Most of the world other than the US doesn't have an automatic upgrade policy, so upgrades are usually only given when required operationally (i.e. a cabin has been oversold). The higher up the food chain you are the more likely you usually are to get one of these, but it is never guaranteed and other pax with lower status can and do get upgraded before you sometimes. The reverse also applies, if someone is going to get bumped or downgraded, the higher up the food chain you are the less likely.
Upgrades are usually something you will need to use points and/or cash to achieve either in advance or at the airport, not free.