Emily - those are pretty good pictures to get the idea! It could be the fruit in that top pic were incompletely pollinated and if they don't fill out, they will probably drop off. There's a good chance the round ones may hang on though since calamondins tend to be precocious once they start fruiting, and sometimes get carried away. lol As long as it gets what it needs - sun/light, warmth, water, and fertilizer, you should hopefully get a few fruit to hang on. The fruit are generally small so they should size up more quickly than the larger-fruit citrus.

If your tee is grafted then yes

Post a picture of the bottom 8 inches or so of the trunk.

Your tree could either be:

1) seed-grown, in which case that's great that it's blooming already. Normally it can take 3 to 5 years from seed.

2) grafted. It would be normal to have fruit now.

3) grown from a cutting. Also normal for it to be fruiting now.

How did you come by the tree?

I think "Jen's Brighter Blooms" mostly sells grafted plants, with the scion perched on top of the rootstock (which is probably something like flying dragon). I have purchased from them before. If you got a smaller one, it was probably 1 - 2 years old (as a graft) and this year might be year 2 or 3 (and since it is trying to fruit, it may be year 3).