Learn Farsi: این یکی گرم است.

The word یک (yek) means 'one'. Adding the -i suffix turns it into a noun or pronoun meaning 'a single one' or 'someone'. When combined with این (in), meaning 'this', این یکی perfectly translates to 'this one'.

Could I just drop the word for 'one' and say این گرم است (in garm ast)?

Yes, این گرم است simply means 'this is warm'. But adding یکی (yeki) makes it sound much more natural when you are choosing or comparing things in a group, just like saying 'this one is warm' instead of just 'this is warm' in English.

If the lesson is about indefiniteness, why does 'this one' feel specific?

It is a mix of both! The word یکی (yeki) by itself is indefinite, meaning 'a one' or 'somebody'. But by putting the demonstrative word این (in) right in front of it, you pin it down to a specific item. Literally, you are saying 'this a-one'.

Can این یکی (in yeki) be used for people too?

Yes, you can use این یکی for both people and things. Whether you are pointing at a cup of tea, a puppy, or a person in a photo, you can use it to single out 'this one'.