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If it's in a container, water at least once a day and 2 times a day in temps over 85 F. Those grown in the ground can be given a deep watering on a weekly basis, around 1-2 inches.

Yes, mandevilla can be propagated by seeds, cuttings, or dividing the root-ball; however, most new plants are produced from softwood cuttings taken in early spring. Here is more information: https://www.gardeningknowhow.com/ornamental/vines/mandevilla/mandevilla-propagation.htm

For more information on cuttings, check this article: https://www.gardeningknowhow.com/ornamental/trees/tgen/how-to-root-cuttings-from-various-shrubs-bushes-and-trees.htm

It is considered in the list of poisonous plants, but allegedly its toxicity is very low, and no severe symptoms would result from ingesting it. However, to be on the safe side, I would try to keep the plant away from them, though these animals normally won't bother the vine. Here are articles with toxic plants for cats and dogs that may be helpful to you as well: https://www.gardeningknowhow.com/plant-problems/environmental/plants-toxic-to-cats.htm
https://www.gardeningknowhow.com/plant-problems/environmental/plants-poisonous-to-dogs.htm

There are a number of reasons why the leaves may turn yellow. One might be overwatering. Too much water causes yellowing of the leaves and mandevilla do not like overly wet feet. Another possibility could be too little water. If this is the case, the yellow leaves would be curling up as well. Mealy bugs can occasionally affect these plants, causing them to become weak and leading to yellow foliage. Finally, plant stress due to a change in location, temp., etc. can lead to yellow leaves. Mandevilla favor humid conditions. If your plant is exposed to the sun, the soil may be too hot. Try misting/spraying the leaves with water in the mornings and keep the soil moist (NOT wet). You may also want to consider moving your plant (if possible) to an area that doesn't receive direct sunlight for extended periods of time.

There are a number of reasons why the leaves may turn yellow. One might be overwatering. Too much water causes yellowing of the leaves and mandevilla do not like overly wet feet. Another possibility could be too little water. If this is the case, the yellow leaves would be curling up as well. Mandevilla favor humid conditions. If your plant is exposed to the sun, the soil may be too hot. Try misting/spraying the leaves with water in the mornings and keep the soil moist (NOT wet). Mealy bugs can occasionally affect these plants, causing them to become weak and leading to yellow foliage. Finally, plant stress due to a change in location, temp., etc. can lead to yellow leaves.

It is likely just the stress from repotting and should right itself once it recovers. However, to help it along some, you can try giving the plant some phosphorus rich fertilizer or add some bone meal to the soil.