Asalamu alaikum please I want to ask a question regarding namaz for those peoples who go from one city to another for a week please kindly answer me . Neelam

Wa aleikumus-Salaam.
If the distance is more than 88kms from your home to the city you`ve planned to travel to, then you are a musaafir. Otherwise you just pray as usual, and the rulings of safar don`t apply to you.
If you are musaafir then, it starts when you start the travel no matter if you are 100 meters from your home or 100 kilometers, and as a saafir you make qasr of dhuhr, asr, and isha. That means you pray those salaat that are 4 rakaa`at only 2 raka`at. Is this clear? So every salaah of a musaafir is only 2 raka`ahs except al-maqhrib, which is as normal 3 raka`ahs.
And you may combine between the times of dhuhr and asr by praying them both between their times (after sun has passed it`s peak, but before sunset is too close - check the approximate times of salaat in those areas and compare them and estimate) when you have the chance one after another (you can make one athan, but both with their own iqaamah). Also you may combine between maqhrib and ishaa such that you can pray ishaa straight after you prayed maqhrib.
From sunnah is not to pray normal 12 raka`ahs nawafil salaat of day and then tahajjud in safar except witr and the 2 raka`ahs before fajr. So make it easy - you get the same reward as you would get for what you used to do at home.
If you don`t find water for wudhu, you know tayammum... Just strike clean ground with your palms, blow the dust off, then wipe over your face and hands, and you have tahaarah. Alhamdu Lillaah.
During the whole week you will continue to be a musaafir (if the distance is over 88km from home) - 15 days is the maximum stay, after which you are no longer under the rules of safar.
If and when you go to pray in a mosque, just follow the imam in your salat, no problem. If you are asked to become the imam however, then you must only pray 2 raka`ahs in dhuhr, asr, or ishaa, and after you make tasliim (saying: "Assalaamu aleikum wa rahmatullaah") the ones that are not in safar need to stand and finish their salaat, but you need to tell them this before you make the first takbiir so that they will know what to do.
And Allaah knows best, but I`m not making this up. This is according to Quran, Sunnah and ijtihad of `ulama.
And Allaah knows best.
Salaam.