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Ходить only implies movement on foot, without a definite direction (otherwise it would be идти).
Гулять means "to walk at leisure, for resting"

You cannot say for example "Пошли ходить!" - it is...

I don't think this sentence is perfect. It would be fine either:
Мы с младшей сестрой любим ходить в парк.
or:
Мы с младшей сестрой любим гулять по парку.
or also:
Мы с младшей сестрой любим...

I agree, but I was looking for a general rule to explain this fact.

As it seems to me now, I am about to conclude the following:

Genitive Partitive is not normally used with Imperfective verbs....

That's not a general rule!

I only meant that "купить хлеба и молока" is OK!
But "покупать хлеба и молока" sounds strange (at least for me), "покупать хлеб и молоко" is preferrable.

So I meant...

Я часто езжу в город, чтобы покупать молоко и хлеб.

But you can also say:

Я часто езжу в город, чтобы купить молока и хлеба.

And it sounds even more natural for me.

However, pay...

So, to summarise movement verbs:

Я иду в кино с моими друзьями

Possible with meaning "I am going now"
If you imply "I go regularly" you should say:
Я хожу в кино с моими друзьями

Я часто...

No, it's not necessarily destructive, as we see it from Lampada's example:


Just влететь in this context means "to fly into a closed space", you can
влететь в комнату, влететь в окно, влететь...