As a Corean citizen you can use a Eurail pass. With an Interrail pass you can only travel on a maximum of 2 travel days in Germany.

If you are traveling within Germany then consider the Deutschland ticket.  It only costs €49 for a month.  Note that it covers regional trains and not high speed, ICE, IC or EC trains.

From seat61.com -

It's not valid on long-distance ICE & IC trains or similar long-distance trains classified EuroCity, TGV, Thalys, Railjet, Westbahn, Flixtrain or Snälltåget.  So yes, you could cross Germany with it if you wanted, but only using slower regional trains.

The Deutschland ticket only covers journeys wholly within Germany, with just a few exceptions:  It's valid on cross-border regional trains to or from Salzburg in Austria, and on cross-border regional trains to or from Hengelo & Enscheda in the Netherlands.

Another thing to consider is to go to the DB office and ask if they have a Germany pass.  Years ago, my husband and I travelled a week from Cologne to Berlin to Munich to Freiberg and back to Cologne with a pass, taking several high-speed, long-haul trains in the span of a week.

The German rail pass and Interrail/Eurail for Germany have been merged into one pass, also available from the Interrail and Eurail websites.

Someone know if I can pay the  Deutschland ticket only from July 8 until August 8 ?

No, Deutschland ticket is always per calender month, so July 1 until July 31.

so what type of ticket can I use for those days ?? Please tell me 

You can buy a Deutschland ticket from July 8, for example via the HVV Switch app. Via this app (and maybe more?) you wil pay the first month only from that day on, so it will be around 38 euro. For the next month you will have to pay the full 49 euro. Remember you have to cancel your subscription before the 10th of a month, otherwise you will have to pay for the next month also.

Ok so uf i understand well I would pay 49 for my 8 days on August and around 36 for the days of July ?

Please remember to cancel the ticket no later than August 10th, otherwise you will pay another 49 EUR for September.