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While I cannot be certain, I believe this is a pencil plant (i.e. pencil cactus) from the Euphorbia genus. In your area, it is best grown as an indoor plant. Here is more information: https://www.gardeningknowhow.com/ornamental/cacti-succulents/pencil-cactus/care-pencil-cactus.htm

Here is a link with growing information and how to grow from cuttings.

https://www.gardeningknowhow.com/ornamental/cacti-succulents/pencil-cactus/care-pencil-cactus.htm

The tiny leaves grow from the tips of the new plant growth and generally will drop off the plant as it ages.
The leaves are normal.

https://www.gardeningknowhow.com/ornamental/cacti-succulents/pencil-cactus/care-pencil-cactus.htm

Cut the branches back to the desired height. Make the cuts at back to a branch union to hide the cuts.
Use clean garden shears and wear protective gloves. The milky sap is an skin and eye irritant.

Use a spray bottle of water to mist the cut areas, this will stop the sap flow.

Wash the gloves and tools after to avoid a issue with touching the sap.

https://www.gardeningknowhow.com/ornamental/cacti-succulents/pencil-cactus/care-pencil-cactus.htm

A Pencil Cactus needs lots of sunlight and very little water.

Since your cactus is still declining, I would consider repotting it into dry cactus mix soil. You can fine premix planting mediums at most garden centers or even big box stores.
If the soil is very wet, you can even lay the root ball out on some newspaper to dry out for a few hours before repotting.
I would recommend a clay pot, as this will help absorb excess moisture.
If too much of the root system has suffered root rot, you may not be able to save the plant.

https://www.gardeningknowhow.com/ornamental/cacti-succulents/pencil-cactus/care-pencil-cactus.htm

The pink tinge or color to the tips of the cactus will disappear as the plant grows and matures.

Here is a link with growing information.

https://www.gardeningknowhow.com/ornamental/cacti-succulents/pencil-cactus/care-pencil-cactus.htm