There are a couple of considerations in your question Kristy. Firstly, have a think about what it is you want to achieve. It sounds like you want to have identical contacts across your husband's devices and your devices, but this isn't the way Contacts works. Although it is not uncommon for couples - or indeed groups - to want to share a Contacts list it isn't the way the software is set up.
Synchronising across accounts has been known to work, after a fashion, but Apple's Contacts app is designed as a one-person utility and cannot be shared with other iCloud users even in a Family Sharing group. This is the opposite to the Calendar app which does permit sharing even between people not in a Family Sharing group.
I have seen someone sign into a partner's Contacts using their Apple Account credentials via Settings > Apps > Contacts, but this is not recommended and possibly contrary to Apple's terms of service as it might have some security issues.
I have never used Google contacts so I can't comment on that, save to say that this too is an IMAP email account service which synchronises between the cloud and a device. This is the same model used by iCloud. Your Google contacts will sync with your Google account. Your iCloud contacts will such with your iCloud account. While both will appear in your Contacts app and appear together but they are actually from different sources, but they remain separate and won't appear in the other account. You will get duplicates if you try to add one to the other, which is what you have found I think.
What I am recommending in a roundabouts way is that you and your husband might consider having separate and independent contacts in the Contacts app, swapping those you might want to share (using email or Messages). This is what I do and it works for us, and I am unconvinced of the virtues of sharing contacts across multiple iCloud accounts, especially with all the trouble it takes to do so.
You are not the first one here to wonder if contact sharing is possible similar to calendar sharing. Send some feedback to Apple at Feedback - Contacts - Apple
Regarding your husband not automatically getting apps available from the purchases in your Family Sharing group - they will be available via the App Store and have to be downloaded.
