I started both my boys on the feed/play/sleep routine at 2 weeks (well, tried too, but they were still pretty sleepy then lol!). 7 weeks is a great time to start, like Willow said it helps them learn night from day so hopefully they will sleep long stretches overnight for you. I do a "dream feed" at 9:30pm where I feed my DS in a dimly lit room, no talking, etc., then I put him straight back to bed after his feed and he has learned to keep sleeping.

For wake time, yep on a mat on the floor, in the bouncer, a walk in the pram, tummy time, cuddles, etc...are all good! Floor time is great for helping to release wind! At 7 weeks your bub may only manage 45 - 60 minutes of wake time. My DS could only handle 45 minutes at that stage so it felt like I hardly saw him! If I tried to stretch his wake time out he would get overtired and would be hard to settle to sleep, then wouldn't sleep properly. It is all a big learning curve!