Question about group giveaways

You can directly enter the giveaway.
Just sync your account before.

after joining a group you have to sync your steamgifts profile, after that you can join the group giveaway(s)

Youg just need to join the group and resync your account here. clicking on Account / Sync Account

With a public group, people can just join the group and then the giveaway if they notice it on your profile. So, if you want a giveaway to be for a certain site of people, others can enter if they notice. And there are people that will enter every group they find just to enter a giveaway.