1 - Group invite
Unfortunately, (as you may already know) you simply can't invite group members to your game directly like the previous CoD games without adding them as friends. I've already reported this soon after the game was released and was hoping there's a future patch to address this [NOT a Steam issue]

2 - Friends not showing up in-game
There's a bug affecting players with more than 100+ friends where you simply won't be able to see certain friends in the lobby due to the limit of 100 players on the list. This has also been reported

Currently, we have no choice but to manually add players that we regularly play with as friends to join. You may use the recent players as well but most of the time it simply won't help at all