Ajax categories problem

I have two problems with the ajax classification:

1.- Home, I use 4 “Block 4” for different categories in my web, and I want to use only the tags that belong to their own categories, I mean if I am in the sports block, I want the tags of sports category, not all. In this image you can see two different blocks, but the tags are the same (category filter option is different), and you can advise the option “Filter by Tags IDs”, I understand that this option chooses directly the tags related, isn´t it?

2.-In another page, I have other categories with “Flex Block 3”, in this situation, If I choose “Filter by Tag IDs” appear a lot of text of the tags that fills the whole area of the block, as you can see in this image. It´s a similar question, ¿How can I choose the tags related with the block´s category? ¿It´s possible to write by hand the categories?

Thanks!

Sorry, because I think I don´t explain right because in all my text I am always speaking my problems with TAGs, not with categories, I want to show in the list the tags that belong to an own category, as I said, if I have a sports category I want to see or choose manually the tags of that sports category, not all or other categories.

I don´t know the answer to my second question also, thanks for all!

But is it not possible to include by hand the tags on this menu??? Because I understand it´s a non-automatic process so is a question of code.

So is there any solution to show the tags in the blocks or flex blocks?

If not, I think it´s very important this option, so I would need some solution even editing code.

Thanks.