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It seems that this tree has been stunted quite severely. The growth is still that of what one would expect from a half year sapling.

With this being said, it could be from 6 to 10 years to see the first flowers and well after that to see the first fruit. So getting it to flower will take time.

The best way will be proper care from here. This will allow it to mature properly. This collection of articles will give you information on the care of citrus in container: https://www.gardeningknowhow.com/edible/fruits/lime/potted-lime-trees.htm

This collection of articles will offer information on how to craft your own pest control with things that you already, likely, have around the home:

https://www.gardeningknowhow.com/special/organic

Greetings, I'm Don in Samut Prakan near Bangkok.
Your lime tree is probably not so big that you cannot reach all the foliage, so one way to control the caterpillars is to remove them by hand, with a rag or a cotton glove, or a water spray.

Or the plant can be sprayed with wood vinegar (available at HomePro or Global House in the garden section and other garden centers and farm supply shops), they also have neem oil concentrate (sadao) which is a natural botanical insect repellent. These need to be repeated weekly.
Or you can use a commercial insecticide like those in aerosol spray cans for ants and cockroaches, at Lotus or Big C and neighborhood shops.

I can't tell from the photo of the leaves if the plant is lime (manao มะนาว) or kafir lime (makrut มะกรูด), there appears to be a secondary lobe forming which would indicate a makrut. If makrut then the leaves are used for cooking and you may not want to apply a pesticide, even an organic one, that may contaminate the taste. Therefore you may prefer to use the mechanical control, hand removal or washing with a strong get of water.

This is a Scale pest infestation.

This article will help you with the treatment.
https://www.gardeningknowhow.com/edible/fruits/citrus/controlling-citrus-scale.htm

This is very common... Iron chlorosis. I recommend having at all times, along with a citrus fertilizer, Dolomitic lime, and iron sulfate. Applying these once a year will ensure that the soil remains conditioned. Additionally, they will do this in response to lack of light from being indoors. All of my citrus must remain under horticultural lighting during the winter where I am. If I leave them out in the room, they will drop all of their leaves and start over in spring. Leaving them with too little light indoors will never allow them to fruit, so you may think about putting them under some horticultural lighting for the winter.

Nope, we are not lying!
Green limes are, in fact, underripe. When allowed too fully ripen on the tree, they turn pale yellow.
The truth is that when you see a partially yellow lime, it’s yellow for one of two reasons: Either it’s ripe and less acidic or other fruits or leaves blocked its sunlight while it was still on the tree.
Commercial farmers don't pick each lime individually as it ripens, They strip all the fruits of each tree at one time, and they do it when the majority of the limes are still green because green limes travel better.

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