Q.Limes dropping off while still tiny
My lime tree is producing hundreds of flowers and baby limes, but none are maturing – they get to about 1/4 inch big, then drop off. The tree is in a pot in warm sunny place. We had 1 lime reach almost full size last year, but the rest never grew past 1/4 inch – what can I do to get my limes to grow to full size?
Your tree needs to be bigger, or older, or both. Right now, it doesn't have the muscle (i.e. roots) to support many fruits. Give it the best care possible, and practice selective blossom and fruit pruning, and you should see more fruits, and the number will continue to increase year after year.
https://www.gardeningknowhow.com/edible/fruits/lime/potted-lime-trees.htm
https://www.gardeningknowhow.com/edible/fruits/lime/is-lime-fruit-and-lime-blossoms-falling-off-tree-normal.htm