How to make 3d curve tangent or continuous to existing surface

Im new to catia however not new to modelling. I am trying to create a smooth continuous surface by making 1st and 2nd vertices of 3d curve in the pic tangent to the surface.

My second question as I discovered is that I made a split surface by using plane as cutting element. After the operation was done I just moved the plane slightly down and the split surface became invisible. I can see the surface when I double click the split operation on the tree but not when I close it. The split is the last operation in the attached file

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Hi friend, good morning!!

Just quick question, what are you release using for this 3d model? because I am using catia release 24!! this is because I can't open your 3d model!!

I hope you, can let me know, what catia release are using, or if you can save in .step.

Thanks,

 
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