Welcome! I've had the same problems with my puppy, who's now 6 months old. I thought he'd never sleep through the night, and didn't until he was about 17 weeks when I left him with my mum for 5 nights (and then only until 7am). He then had a relapse back with me, waking up usually around 5.30ish, sometimes earlier. He eventually got a bit better and about a month ago (at 5 and a bit months) we decided to try leaving the cage door open. What a difference! He now sleeps through the night, until at least 7.15. He was sleeping in until 8.45 some days (I've even had to wake HIM up!!), but then the clocks went back, which meant he woke a little earlier, and now we've just changed him on to only 2 meals a day and he seems to be waking a little earlier (usually 7.30-8). I'm trying to give him his second meal a little later so he'll sleep in a bit longer!
One thing that did help was changing his food. When he was much younger I fed him Hills Science VetEssentials, and he was pooing about 8 times a day. So no wonder he needed to get up at 4am! (sometimes he needed to go out twice - grrrr). I changed him to Barking Heads and now he goes about 4 times a day. I think that, together with just getting bigger and having a stronger bladder, helped a lot. When he's had the odd upset tummy I've given him boiled chicken and rice and that totally blocks him up (doesn't poo for a day!) and sleeps just fine...
I still have some problems with walking, although generally he's okay now. He does what Oscar does - just sits down or sticks his stubborn little legs firmly in place! We used to carry him quite a bit, and still do now sometimes. If he doesn't want to leave the park where he's been playing he sometimes needs to be carried. It used to be the worst in unfamiliar places (turning a corner - uh-oh!) but now he seems fine in unfamiliar places, and is worse just near the house if he wants to go in a particular (other) direction. Just try to stay patient, not worry too much, and it will get better with age, I'm sure. Do try to vary the routes you take him on, so he doesn't object going in other directions. We also try to take Henry to unfamiliar places and on public transport so that he gets used to the new.
Looking forward to seeing photos! Good luck - it does get better with age (and then you miss how tiny and cute they were!)