The Drunken Typist

Röda, 720 789 bytes

{K=[["`~1!2@3#4$5%6^7&8*9(0)-_=+","		qQwWeErRtTyYuUiIoOpP[{]}\\|","..aAsSdDfFgGhHjJkKlL;:'\"","..zZxXcCvVbBnNmM,<.>/?.."]()|[[(_/"(?=(..)*$)")()|[[_,1]]]]]K[0][-1]=["ä",2]K[1][0][1]=1.5
K[1][-1][1]=1.5
K[2][0]=["ö",5/3]K[2]+=["
",1.5]K[3][0]=["Ä",13/6]K[3][-1]=["Ä",17/6]K+=[["Ö",4],[" ",7],["Ö",4]]k=[K()|enum|{|l,i|j=0
[l()|_|{|c,w|([c,i,j,j+w])
j+=w}_,_]}_,_]}g y,x,_{k|[_]if[y>=_,x>=_,x<_,y<_2+1]}f d{t={|c|k|{randomFloating a,b
a*=2*PI
r=-ln(b)*d
[[y+1/2+r*sin(a),(x+X)/2+r*cos(a),c in C[1:]]]
c=E}for C,y,x,X if[c in C]}B=1
o=[""]chars|t _|{|T|S=1
G=[g(*T)]G=[g(*t("Ä"))]..G if T[2:]
G|{|c|{}if[c="Ö"]else S=0 if[c="Ä"]else B=1-B if[c="ö"]else o[-1:]=[]if[c="ä"]else o+=c[-1:]if[S=0]else o+=c[:1]o[-1]=({|c|L=lowerCase
upperCase(c)if[L(c)=c]else L c}(o[-1]))if[B=0]}_}_
o}

Try it online!

It can probably be golfed more...

Edit: fixed a bug (+69 bytes)