1. To help her use the online application
That looks fine. It's not a full sentence, but you could say this in an answer to a 'Why?' question.
NB You can either say 'help someone do something' or 'help someone to do something': the 'to' is optional.
2. He's looking for a shop in this town.
If he's looking for one shop, we say 'a shop'; if he's looking for several shops, we say 'some shops'. *
There's no need to add 'here'. The word 'this' is enough to specify which town you're talking about. The only time you'd say 'This town here' is if you're pointing at a map.
*[NB There are a few contexts where we would use 'some' with a singular noun, often to convey a negative attitude. Don't worry about it here, though.]