Greetings @Foxparadise,
First, welcome in PRO!
Then, concerning your question, there is no bug concerning item variety. The more you'll get badges, the more items will be available!
If you need to heal more during battles, you should go back more oftenly in pokecenters. You will also save money!
I also invite you to check the different weaknesses of pokemon to avoid taking big damages!
And to catch pokemon, to make it easier to catch, I advice you to get the closest you can to 1hp, then use a status move, like sleep or paralysis.
You can also purchase the TM False Swipe in Dpt Store. In Kanto, it's located in Celadon.
False Swipe will prevent you to faint a wild pokemon. It will let them at 1hp.
Know hat Farfetch'd and Cubone can learn it by level up. They can be caught in areas close to Lavender City.
Kind regards
RockyRaccoon