## Python 3 (<s>164</s> <s>194</s> <s>186</s> 181 bytes) ##

 p=0
 x=input().split()
 w=x[0]
 for i in x[1:]:
 if i[0]=='+':w,p=w[:p]+i[1:]+w[p:],0
 else:
 try:p=w[p:].index(i[1:])+p
 except:p=len(w)
 w=w[:p]+w[p:].replace(i[1:],'',1)
 print(w)

Example demonstrating the pointer moving to the end if it doesn't find a substring:

 Input: HelloThere -x +Friend
 Output: HelloThereFriend

Old answer:

 p=0
 x=input().split()
 w=x[0]
 for i in x[1:]:
 if i[0]=='+':
 w=w[:p]+i[1:]+w[p:]
 p=0
 else:
 p=w[p:].index(i[1:])+p
 w=w[:p]+w[p:].replace(i[1:],'',1)
 print(w)

Example demonstrating the pointer works (all the examples in the Q work even if you don't factor in the pointer and simply replace on first occurence):

 Input: HelloThereCowboy -r -e -y +ySays +Oh
 Output: OhHelloTheCowboySays

Edit: Since 2 minutes ago my answer is now invalid according to a comment by the asker.

> aaa -b +b would result with aaab because the pointer would go all the
> way to the end.

Edit2: Fixed.