"Watch the episode" is a simple command. It is direct and so could be rude, depending on the context.
"Do watch the episode" is rather rarer. It is a request, normally used in a particular context. Consider:
Here is your cup of tea, and do take a biscuit.
In this example I know 1) Most people like to have a biscuit with their tea, but 2) people will ...
The imperative in English uses the same form as the bare infinitive:
Don't watch TV.
You can see in the last example that when forming an imperative with a negative verb, the helping verb "do not" is used. All these imperatives are likely to be talking about future activities. When you say "Play tennis!" the action hasn't ...
In English, it's customary to use the simple future, for making promises, especially promises made on the spur of the moment.
Mother: Be careful driving the car
19-year-old son: I will, Mum.
Father: Don't be late back home.
17-year-old daughter: I won't, Dad.
The OP's short dialogue is similar
A: "I have to go shopping this afternoon."
So what you seem to be having trouble with are tenses. The present simple tense can be used for things that happen regularly, sometimes, or never, but also for commands.
Don't do that!
I sometimes do it.
I never do so.
1 is a command, whereas 2 and 3 are not. "Don't forget the bread" is a command, just like 1.
Now, when the person listening to the command ...