Hello and thanks ahead of time for all help given.

How do I complete the 3-5-10 part daily quests.  I feel I have completed many, but it doesn't record, and I am completing them as daily quests.

How to I complete the achievement "Explore the many gifts hidden object scene 10 times.  I haven't a clue.  

Thank you all for your time.  

 If I remember correctly, the  3/5/10 DQs only count in non event times.  They will not show on your achievements unless you have completed all the parts of the DQ by change of day.   It is easy to forget to complete a DQ especially if they want you to send several airships or to visit the same HOS several times.  That is where no cool down purple/lilac globes that you sometimes get from an HOS come in handy.   

The many gifts HOS in the Anniversary Room is a non-achievable event until the Devs activate the Anniverary Room,  The only time it has been activated so far is for the 5th Anniversay.  Hopefully, since we got some anniversay diamonds, it will happen this year.

Jerseykaren said:

How do I complete the 3-5-10 part daily quests.  I feel I have completed many, but it doesn't record, and I am completing them as daily quests.

Here is an excerpt from the Archivist section of the MC Game Guide: (It's called that because of how the developers listed it on one of their help sites that's no longer available)

The Archivist – These are the Gnome quests. There are 3 different gnomes that will offer quests to you: Librender the Archivist, Mechanogle the Engineer, and Potionmant the Alchemist. This feature is unlocked at Level 10. 

Pay particular attention to the circle around the Gnome! The Gnome quests are divided into parts…..there are 3-part quests; 5-part quests; and 10-part quests. The circle around the Gnome’s head will have some triangles separating the sections. If there are 3 sections (2 triangles), you have received a 3-part quest. You earn coins, an HOS item, and pet medallions when completing each part of the quest. 

After you have completed the entire quest (all parts), you receive a bonus chest. The chest can be bronze/iron, silver, or gold. There is a separate thread/file that lists what is required for all parts of a daily quest, as well as the type of chest you will receive upon completion.  

Here you'll find a list of the Quests.

Daily Quests and Rewards [midnightcastle 29.1] (delphiforums.com)

Just know that a few years ago the developers created "random" quests. In other words, the name of the quests remains the same, but the HOS/ZZ you visit will now be random. The Play Dice, Fortune Wheel, Feed Pets, and Airship tasks remain the same.

The Elf Quests during the event don't count towards the Daily Quest achievements.