「に、へ、まで」the difference in use with verbs


Well. I saw some topics here on same subjet, but I still didn't get the full
image of a rule.

に - iplies the place, where is purpose-action will take place (final
destination)  
へ - implies the direction of where we are going  
まで - implies the limit, distance or time we're on the move to the place

**Am I correct?**

* * *

But I also have noticed that they are used differently with berb 行く, 来る и 着く.
**に, へ** - if the place is final destination, like when I'm going to the
station to meet a friend.

> 駅 [に・へ] 行く。

**まで** - if the place is just a part of the trip, like when I'mgoing to the
station to take a train to other station.

> 駅まで行く。(ex. to take the train for Shinjuku)

**Is it so?**

* * *

The next qustion is using them with verbs 歩く, 走る and 泳ぐ. Some grammar web-
sites says I can use only まで with these verbs.

> 駅まで走る。

**Is it also correct?**

