Do I need other EP to play B&H to the fullest?

No. Only if you wish to do things such pet cafee. Then yes, you need cats and dogs.

You don´t need:

for rent

get to work

dine out

But you will not be able to make rented flats on top of small business, nor proper restaurants in small business not vets EVEN if you have the packs. Just making sure you are aware of it.

Yes, you will be able to sell some stuff with only this ep. No need of get to work.

Yes and no

No because you can have loads of possible businesses without additional EP. You can own a pool, bar, cafe, shop, tattoo parlour, art gallery, gym,... and many possible combinations of base game activities. There should be a lot to do with just this pack

Yes, because packs will give you even more options like run a pet cafe, spa, laundromat, occult cafe, .... There is a lot of pack integration. I look at it as a little extra for people who own more DLC, not as a requirement to enjoy the pack. 

To the fullest, probably yes.  Here's an article on all the cross pack features for Businesses & Hobbies,

https://simscommunity.info/2025/03/05/businesses-hobbies-cross-activities/