Less than 2 weeks old Instinct does not always synchronize and other things

5959947 said:

During this time it froze once - I had to restart it;

Make sure you run the latest firmware v12.20 (see it in the Settings » About), and update the watch over Garmin Express if it is not the case. There were some freezing issues with the Solar model, but because you post here, not to the solar forum, I assume you own the non-Solar version.

5959947 said:

three or four times is did not want to synchronize with Garmin Connect

There may be countless of reasons, mostly on the side of the phone, that can cause connectivity problems. Check out the Sync / Connection Troubleshooting Guide to get the idea what may went wrong in your case.

5959947 said:

Also, the battery, with GPS on, lasts barely 6 days,

Instinct specification tell up to 16 hours in GPS mode, so 6 days is far more than the specs promise. However, I doubt you really had the watch continuousely in GPS mode for 6 days. That's not possible even in the Ultra Trac mode.

5959947 said:

And twice it did not collect or send data about the sleep time to Garmin Connect. 

Did it record the HR? If not, then perhaps you did not have the watch tight enough, or the syncing failed, or you have accidentally associated the watch with multiple accounts (a very frequent problem), ... there are plenty of possibilities again, so you'll need to provide more details if you want to find the reason.