In english you can use both 'and' or 'or' depending on what you are saying.
1/ will probably appear in longer sentences which are compounded of some number of shorter sentences with a number of "don't"s, "didn't"s, etc...
2/ will appear if you are talking about something as a unit (as a one thing).
'or' will probably appear in sentences which are not compounded of while short sentences.
I'll use some examples to clarify what I mean:
I don't like apples or oranges but I'm fine with grapes.
Here 'oranges' is not part of a compounded sentence thus 'or' is used here naturally.
Now let's take a look how to change it to have 'and' present:
I don't like apples and I don't like oranges but grapes are fine.
As you can see now 'and' connects two independent sentences. While in the example before 'oranges' needed first part of the sentence to make sense ('I don't like').
Note: Of course you can have longer pieces of text put together with 'or' too as long as they are dependent.
Lastly, using 'and' to form a unified image:
I don't like apple and orange mixed juice but I'm fine with either apple or
orange one separately.
Here I'm talking about a unit of apple and orange juice together while I can still have a different opinion about each of them.
Natives prefer or because it's shorter, unless you have a special reason to go a different way.
Lastly, I'd like to mention other possibilities which are commonly used:
I don't like either apples or oranges.
I like neither apples nor oranges.
So your sentences would probably be better with just 'or' unless you are trying to express it as a unit as explained above.
This is what I was taught perhaps somebody can clarify it better.