It'll not go well for your character
From your description we can infer a few things. One is that your own character is unaffected. The other is that everything else in the area is affected.
First let's disregard the character. The time slow is dangerous. Imagine standing just outside the zone and grabbing a hose. Squirting some water in will slow that water, causing the faster running water behind it to run into it. This'll create a lot of pressure on the water as it tries to escape. Many forces from outside should approach carefully and not too much. Wind, a river, water in pipes and more can seriously mess up/explode, especially if the time stops being slowed.
Gravity is tricky, but from what I understand it'll not be like the hose. Normally gravity is instrumental to time dilation, so it's difficult to infer what will happen if a time slowing where gravity isn't instrumental. From my limited knowledge it wouldn't be like the hose. The gravity is constant, regardless of the speed of time. So the gravity of the earth will be constant and not increase like the hose. In other words, slowing time down to half will not increase the gravity to twice as much.
Now the character. She/he has to have an aura around him/her, or get a very bad time. Clothes and even the air would imprison them. If the character would try to move without this aura he/she would feel the friction of moving x tines as fast. In addition, they would barely be able to draw a simple breath. If a normal time aura extends outwards they still should keep moving to prevent circulation of the breathed air and getting CO2 poisoning. Fresh air is important.
But moving creates many risks. A door partly inside the personal aura will have the same problems as things from the outside of the time zone trying to get in. He/she opens the door and is likely to break it, as they will apply force like a lever against the door. She/he is applying in a half time zone basically twice the force in a time frame on the part of the door outside the aura. Now imagine items flying around with a tremendous force and coming into the aura, speeding up and striking the person. Not a good time.
As for gravity for the character it seems clear. The character will have the same force applied, regardless of time. Someone might correct me on the gravity part still (and they're welcome to). Yet it is dangerous any other way. Lower gravity can mean moving requires a fully different way of handling, while if the same amount of force from gravity is applied over a shorter time to the people in the time dialation they would experience twice gravity with a half reduction.
But walking on walls is never practical. If you push yourself off the surface, you need to have a way to get down again. In a hamster wheel it's fine and dandy, but if the hamster wheel is sideways so you have no gravity pulling you towards the surface you push off from it'll be near impossible to stay there. Of course they'll be able to do some forms, as you can see people do great gymnastics from (slanted) walls, but moving like Quicksilver is unthinkable. But as the time isn't slowed for the character I see no reason why she/he wouldn't just fall flat on their face.
In my examples I often was referring to slowing down time by half, making the character twice as fast. Quicksilver goes many, many times that, as he can outrun bullets with ease. With increase of the time slowing, the problems get progressively worse. Although above are some major simplifications of the problems, you can assume that slowing down is very dangerous and should be done very carefully, or have some extra magical rules that make it work.