I work in the space, and I'm not sure that there's a Personal CRM product out there that does all of what you're looking for.
One close option would be Contactually. Where it meets your requirements:
- Aggregates information about contacts from connected social networks. I'm not sure if it sends that data back to Google Contacts or not - would be worth looking at.
- Lets you set up alerts to follow-up with contacts.
Where I'm not sure it meets your requirements:
- Shows all of a contact's social media updates. It cannot do this. However, this isn't as strike against Contactually - to my knowledge, there's not an app out there that can do that anymore, due to terms of service restrictions from Twitter, Facebook, and LinkedIn.
- Normalizes contact information. (It may do this - I just can't remember if it does.)
All-in-all, if the CRM-style reminders is the biggest priority, Contactually would be a good option to check out.
Another option would be FullContact (who, in full disclosure, I work for). Again, it doesn't meet all your requirements.
Where it fits:
- Aggregates social profile information about contacts and syncs to Google Contacts. It definitely offers 2-way syncing of social profile links, images, etc. to Google Contacts.
- Normalizes contact data. It cleans your contacts to make sure they're all in the same format, and syncs them all back to Google Contacts.
Where it doesn't fit:
- Sets up email alerts to follow-up with certain contacts. FullContact isn't a fully-featured CRM - it's more about enriching, de-duplicating, and cleaning your contact data.
- Shows all of a contact's social media updates. (Again, this is due to the TOS from Twitter, Facebook, and LinkedIn, most of which no longer allow their updates to be extracted in that way.)
So it really depends on what you need most. It sounds like Contactually would work best for you, if you're looking for a personal CRM that will manage your relationships with contacts (and it may sync that data back to Google Contacts, too).
If you want an app that adds social profile information to your Google Contacts and normalizes them, FullContact may be what you're looking for (again, full disclosure, I work for them, so I'm biased). But it sounds like Contactually is more what you're after, anyway, due to the CRM functionality - I'd start with them.
I can't think of an app that does exactly what you're looking for - but either of those two options will be close.