Elliot won't take the gift's you try to give him why is this?
Elliot probably won't take it because you neglected him.
In IOH, you can't neglect the main characters (ie; not talk to them) for more than two days before they get miffed, and won't accept gifts. I learned this the hard way myself, and ended up googling a good FAQ that had the information i needed and then some. The good thing is this shouldn't happen if you forget them for just one day or so, so it's not as big a bother as it could be.
If you've neglected them for three or four days in a row, then you have to talk to them for that same number of days before they start accepting gifts from you again.
It's only for the 'main' island characters that this happens though i think, and the maximum number of days they'll stay miffed is five (aka; talk to them for five days straight and if you've ignored them for even a full season, all is forgiven.)
So it's a good idea to talk to someone every day a week (or just the five days) before an event like their birthday or a gift-giving holiday (visible on the calendar) to make sure that they'll accept your gift. Because it still counts when it comes to giving gifts, holiday/birthday or not. Even if it's their absolute favorite gift.
For the Subsidiary characters (Those not-so-important ones like the random fishermen, miners, farmers, ect. that show up whenever you've completed so many goals or for other reasons.) though, it's not the case. They'll always accept gifts, but if you neglect to talk to them at least once a season they'll go away for a season, and/or until you've met certain goals to bring them back (like shipping more fish for some of the fishers, or so many mining items for the miners. Or giving the harvest goddess so many gifts before some of the churchgoers reappear).
It's a lot easier to talk to the non-main characters once a season than it is to try to bring several back when they disappear on you. Some are seasonal though, but this is for the others who aren't and are usually there year-round or daily.
Here's the link to what i learned this from. It's also got tons of other useful tips and info to use.
(and in case that didn't show up, http : // faqs . ign . com / articles / 903 / 903040p1 . HTML --just delete the spaces)
And this is the website that that link is on. It has links to character guides, the FAQ above, Recipe guides, Likes and Dislikes of the characters so you can give gifts that the person likes better and reach whatever heart you're aiming for quicker blah blah blah and all that good jazz. ;)
(Again in case that doesn't show up, I've never used this site before so i don't know: http : // faqs . ign . com / objects / 848 / 848020 . HTML --delete the spaces)
And quick tip--for the horse and dog, make Chen the storeowner and Mirabelle the owner of the ranch store two-heart levels (giving gifts to them is good, but buying something from their store should have the same effect as a gift). Chen should just give you the horse one day (You might have to raise his son's heart levels to two as well, I'm not certain.), and for the dog you've got to enter to the west part of the island once that bridge is completed on a rainy day and Mirabelle will find you and you'll both find the dog. And get the old guy Taro at two hearts by giving him wild grass (doesn't matter the color, and two hearts should take less than half a season if you give him one every day) and he'll show up with the fishing rod. I hope this was helpful, and if you need more help you can probably find me on fanfiction as Ashen Rose, though the two links should have everything. Good luck gaming!