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Any pictures would be very helpful. The first thing I would check is the pH. dolomitic lime (I like Agri-pel, and in Tennessee it is only 5 dollars for a 40 lb bag. This will stabilize the pH of the soil) Other issues could include over fertilization, Overwatering, or incorect temperature. I believe it likely to be incorrect pH, Over fertilization though. Check first.

Yes, there is a way to do this. This can be a bit more tricky than cloning in soil, however, with the right tools, you can do it easily. the best way to achieve success with this method is to have the water always moving, and always oxygenated. The easiest way to do this is to put an airstone attached to an air pump into the water at the bottom of the container. This can be a simple aquarium pump and does not have to be big, The next step requires some sort of hormone, or rooting solution. Personally I have had great results with both crushed up aspirin, and honey. It will not hurt to use both at the same time. This will bring your success rate way up! It is necessary to change the water, and solution about every 3 days or so. If you need more assistance with this subject, please do not hesitate to post more questions here. Welcome to the world of hydroponics!

I'm not able to see the photo you uploaded, unfortunately. But here are some possibilities for what might be going on:

https://www.gardeningknowhow.com/ornamental/vines/mandevilla/yellow-leaves-on-mandevilla.htm
https://www.gardeningknowhow.com/plant-problems/environmental/plant-leaves-turn-yellow.htm

Mandelvilla are tropical plants that can't survive outdoors in zone 5 winters. They can be lovely winter houseplants, though. These articles should help:

https://www.gardeningknowhow.com/ornamental/vines/mandevilla/growing-mandevilla-indoors.htm

https://www.gardeningknowhow.com/ornamental/vines/mandevilla/winterizing-mandevillas.htm

Unfortunately, these are only hardy to zones 9 and up. They won't require a winter dormancy. They need to be kept at no lower than 60 degrees to grow healthily. The best plan of action would be to grow it indoors during this time. Place it in a Sunny location. It is best to be on the south side with a south facing window, if that is possible.

Here is an article with more information: https://www.gardeningknowhow.com/ornamental/vines/mandevilla/winterizing-mandevillas.htm

This depends on where you are located. This is a tropical, so if it gets cold, then I would bring it in as it isn't likely to survive outdoors. Here is an article for more information: https://www.gardeningknowhow.com/ornamental/vines/mandevilla/winterizing-mandevillas.htm