I would like to see a search option within my own tree for different things; specific war, occupation, immigrant, name (sometimes I remember the name, but not where they are in the tree), etc.
This is a very frequent request/suggestion, but it's unlikely to be implemented any time soon. The problem is, how should FS define and delimit what's "yours"?
Should it come up with a subset of the tree before every search? When you download such a file, it can take several hours, depending on how many generations of ancestors you want, and how many generations of their descendants.
Or should it do the search first and then run the "find my relationship" routine on every result? That could make each page of results take several minutes to load.
If you're looking specifically for an ancestor, then your browser's "find on page" function on the fan chart should do the trick.
If you've edited the profile in any way, then it will be on the "My Contributions" page, which can be searched by name.
For complex or detailed queries like occupations, offline family tree software is your best bet. There are several that can fully synchronize with FamilySearch's Family Tree. As I wrote above, downloading the data into such software can take a while, but luckily, you only need to do it once.