Yes. Going slow is an advanced skill. Clinging to a fence inhibits learning. Learning is much less about balance than keeping the wheel under you.
Sounds like you need to get your weight in front of the wheel so you can ride away.
Have a look at unimyra’s video.
Don’t try too hard at free mounting yet as it can be frustrating. It will get easier as your general riding skills improve, particularly riding slow and still stand. Better to work on getting more control of the uni.
Focus next on steering by leaning the uni with your hips rather than twisting. At first you lean the uni in the direction you want to go while counter leaning your body to stay above the contact point. Later you will learn to lean your body into the turn.
And work at getting most of your weight on the seat.