"개가 빵을 조금 먹습니다."
Translation:The dog eats a bit of bread.
They are both using the -ㅂ니다 formal ending. We use 습니다 when the end of the verb we are conjugating has a consonant, and ㅂ니다 for any verb with no ending consonant. 합니다 is the ㅂ니다 added to the 하다 verb, which means "to do"
With no ending consonant:
가다 -- 갑니다
오다 -- 옵니다
With ending consonant:
먹다 -- 먹습니다
늙다 -- 늙습니다
Present, past, and future of 하다:
하다 -- 합니다
했다 -- 했습니다
할 것이다 -- 할 겁니다/할 것입니다
Yes and no. It technically changes the meaning, but in this case, the change is almost meaningless.
If you say 조금 빵, it means a little bit of bread. If you say 조금 먹습니다, it means the action of eating is minute or small. So if you change the position of 조금 in this sentence, rather than meaning the dogs doing the action of eating only a little bit, it would mean a little bit of bread was consumed, regardless of their eating habit.
But, as you can see that I struggled to explain the difference (if I even did well at all), it's such a small change in this sentence that it's unnoticeable :P
"The dog eats a little." would mean that the dog eats a small amount.
"The dog eats a bit of bread." means that the dog eats a small amount of bread. We don't know if the dog eats a lot of something else.
This sentence does not talk about the duration of time that the dog eats, which is what your second sentence does.
There are many different ways to end verbs, in informal, formal, and honorific ways. Here's a great website to learn about all of those forms and many different grammar points and the nuances within: https://www.howtostudykorean.com/
Another great website for verb forms is: https://koreanverb.app/
And finally, another really amazing website that probably far exceeds the others: https://endic.naver.com/search.nhn?sLn=en&dicQuery=hello&x=0&y=0&query=hello&target=endic&ie=utf8&query_utf=&isOnlyViewEE=N
Hopefully these help you in finding out more about verbs. If you have any other questions, feel free to reply!