1) Your usage isn't strictly incorrect, but it sounds awkward. You'll more often see, "I will walk to there, then start running." We drop the duplicate "I will", the 'and', and the "as far as". These words are all implicit in the sentence.
2) This is perfectly fine. Sometimes you'll see 'provides' instead of 'does', but it only really changes the level of formality. A bundle is a group of things attached together. When we talk about service bundles, we are saying that multiple services are combined (usually at a lower cost), all with the same contract. So AT&T* would offer their all-in-one bundle, which provides phone, TV, and internet all in the same contract.
3) The only thing I would change about this sentence is the part after the 'and'. I would say, "and then it begins to climb." The first part of the sentence works with either 'runs' or 'is' and with either "up to" or "as far as".
4) Use "on the upper part of the map". As far as your arm goes, you use whichever more accurately describes the situation. If someone punched you, you probably feel pain *in* your upper arm. If a bug bit you, you probably feel itchy *on* the upper part of your arm. Usage of 'in' is much more common, since pain is always in your body, not on your body. More often though, people will just say, "My upper arm hurts!"
*Strangely, italki filters the ampersand (&) into a pointed bracket (>).