Branches are close to 3 ft long. They are so flimsy they actually touch the ground when it rains.
Your tree needs to be pruned to grow healthier. Here's an article that will help:
https://www.gardeningknowhow.com/edible/fruits/plum/plum-tree-pruning.htm
These lumps are appearing on the plum tree leaves, but no signs of insects. What could it be and how do I treat it.
They are, certainly, from insects. Usually mites or midges cause these types of galls. This isn't as bad as it gets, and is a fairly mild case here.
It isn't going to harm your tree that much. It may be unsightly, but treating for mites or other insects to prevent future infestations will be the only method of control.
Here is an article to help you to combat leaf galls:
https://www.gardeningknowhow.com/plant-problems/environmental/treating-leaf-gall-on-plants.htm
The leaf buds have only slightly swollen and show no green. I can see the sap collecting at the base of each bud
unfortunately, your photo did not come through. I am unable to see the issue.
I can say that many plums are only suited for our USDA zones 5-9. Most of your country is equivalent to our zone 9. Depending on the type of plum, it may not have received enough chill hours through the winter to come back out properly. Some are not as tolerant of lack of freezing weather as others.
Here is an article to help you with plum care:
https://www.gardeningknowhow.com/edible/fruits/plum/growing-plum-trees.htm
What can I do so this will not happen next year? The tree is about 12 years old. There is a clear jelly inside the seed.
This is, mostly, caused by grower interaction. Any attempt at a larger fruit than is allowed by the tree by, or overfeeding/watering, or any significant changes in care can cause this. Once conditions return to their proper state, the fruit will return to normal.
Here is an article that will help:
https://www.gardeningknowhow.com/edible/fruits/fegen/stone-fruit-pit-split.htm
The new fruits are mal formed like mummified,I was told to spray with fungicide,but I don't know which one??
Sorry to hear about your plum trees. We don't make brand recommendations, but use a fungicide like lime sulfur, chlorothalonil, captan, thiophanate methyl or myclobutanil.
Here are a couple articles that may be helpful:
https://www.gardeningknowhow.com/edible/fruits/plum/treating-brown-rot-in-plums.htm
https://www.gardeningknowhow.com/edible/fruits/plum/plum-tree-diseases.htm
Do I need two plum trees or can I use the other citrus trees already planted in the yard for pollination?
It would depend on the variety of plum that you have. Some are self fertile and some are not.
For a tree to cross pollinate they need to be at least in the same genus. Many times they even need to be the same species, but this is not always the case.
https://www.gardeningknowhow.com/edible/fruits/fegen/self-pollinating-fruit.htm
I purchased a plum tree a few months ago, there is no life in the branches, they look like dead twigs, the tree is not dead as there are shoots appearing at the bottom. What should I do.
If the shoots are from the bottom, that means they are coming from the rootstock. The desirable tree may be gone. Here is more: