Yes, its the same. Let me give you some examples using both: یه جمله مثال می زنم. یک جمله مثال می زنم I'm giving you an example. یه سیب خوردم یک سیب خوردم I ate an apple. یه روز پیش دیدمش یک روز پیش دیدمش I saw him/her a day ago.

Yes, its almost the same, but dont forget that for counting we always use. Yek = one But "yeh" its like "a/an" in English.

adding to other's answers: One can also be translated to "ye" one more thing یه /یک چیز دیگه ye/yek chiz dige Mother tells to her little son who is taking 3 candies: you can take only one faghat mitooni ye/yek doone bardari (Here we dont need subject (you) in Persian translation) فقط می تونی یه / یک دونه برداری

the same meaning but yeh is used more in spoken Persian. and what Tany said is correct. by the way "yek" is formal which used both in spoken and written .