For a week old baby this is normal. Baby is not sucking due to hunger. They comfort suck at this stage. Moreover this will also help you to establish a good milk supply.

Yes,no issues even if you pump and feed but that won't assure that your baby sleeps at night! Your baby is too small and expecting him to sleep at night is not fair until at least 6 weeks. At this stage ,milk supply is low only that's why it's important to latch your baby as frequently as possible,the more your baby suckle,you will get that much supply. If your baby is suckling nipples at night for that long,just see if he is latching correctly. At this age baby needs a lot of comfort,warmth,live and needs to be held close to mother. So no doubt he would do this. For you,if you want manage,sleep at day time when baby sleeps and work (feed) in night. Make up your mind that you will have to be up at night. Slowly start a routine with kid before bedtime but not until ur baby turns at least 6 weeks. All efforts prior to that might be futile and then you will again be frustrated! Happy feeding! Let us know in case if any questions