Reducing the size of the search field should be as simple as changing the bootstrap size value from say large to medium, or medium to small on your search input. Getting everything to the left shouldn't be too difficult either. You should be able to set a css class for your container by right clicking on the widget and going into edit container. Change the container class to something like "search-class".

From there, you can go into your page-specific css and set the text-align property to left and override any other properties like this:

.search-class{

text-align:left !important;

}

this SHOULD throw your text and search input to the left, depending on how things are laid out in your html. The important should override any preset css values further up the hierarchy chain. All of this depends on whether you have cloned the widget or if it is OOTB also.