Array using curve

Yes, you can get rid of those gaps, if I understand you correctly. You just have to make sure the object you are using starts the same way as it finishes, so the beginning and end match and you get rid of the gap. Objects that have to follow along curves can get tricky. So if you can't get around on solving it, maybe you can post screenshots and describe the situation a bit more so we have more context to determine what is happening.

Perhaps if you enable the "Merge" option in the Array modifier, it will merge the vertices and get rid of the gap. Try that.

Yes, but I think you'll have to manually tweak the ends of the curly curves in Edit Mode, to make them fit as closely as possible and add a Weld Modifier at the end of your Modifier Stack to Merge them.

You can also Scale the Radius (with ALT+S) of the endpoints of the Curve, to get a better match.

I don't think there is an automatic way to connect them.

Well, it's a bit messy for sure. You have to tweak it way too much, to the point that it crosses that threshold where it's better to start again from scratch, otherwise you'll just spend too much time fighting and wrestling with it. So I say start again and set it all properly. Try working with your guide mesh aligned to the world, you have it tilted and that difficult things too much:

Also try for the curve and the mesh to line up so it's easier to guide the object. Remember to get the object origins to be in the same place. You can watch the MODIFY course so Paul can break it all down for you as well, he has lessons on curves and array.