All good news!
Practice along the counters as you've been doing until you feel balanced and steady.
It is scary to take those first steps unassisted, you have the feeling the prosthetic isn't going to hold you and you'll land in a heap on the floor.

At least I felt that way, lol.
Remember when you navigate stairs - Up with the good leg first, followed by surgical leg.
When you go down - Bad leg (surgical) first, followed by good leg.
"Up with the good, down with the bad"
Don't forget the heel-toe walking to lose the limp. Heel strikes the ground first, followed by toes.
I feel more in balance when I concentrate on walking that way.
It feels odd at first but try to remind yourself of it as you walk.
The fatigue is Energy Drain. Your body is using all of its energy to heal and not leaving a lot extra for all the other activities of daily life.
https://bonesmart.org/forum/threads/energy-drain-for-thrs.12415/
Rest or nap whenever you're tired, or able to. You're very early into your recovery and there's a lot of healing to still happen.
You can use the belt from a bathrobe (any belt would work) to assist in lifting your leg until it becomes easier.
You're doing great! I hope you have a wonderful week!
@Hip2BGone