Friendship levelling up query

It seems like yes, you progress every time an action is taken on the day, even if all in the same direction.

I'd suggest you just check your progress every day (slide to the next friendship rank on that friend, and it tells you how many more days you need) - if it doesn't credit you for a day, perhaps there's a "one way cap".

As long as they are opened then it will be fine.
If you send every day and they don't choose to accept then you will not level up.
...but if you send it one way, and they accept everyday then it appears that you both will continue to improve your friendship status with each other.

Best I can tell, if you send someone a gift that they don’t open, nothing else you do together (battle, trade) will get YOU points towards friendship until they open it. But the person who received and didn’t open the gift can get points from a battle or trade with you. So friendship growth is not symmetrical.

Case in point: I sent a friend a gift on day 1 that he didn’t open until the next day. We traded that night and then raided together the next day. Now, I still have 5 days of playing together with him to get to Great Friends status. But he has only 4 days of playing with me. This has happened with several of my friends. Seems a bit broken.