The following answer may not apply for a Google Apps for
Education account but only for a normal (consumer) Google account.
There are different ways to do this depending on what you want to achieve.
For example you could:
Delete items individually
Delete related activity
Delete activity using search & filters
Delete activity from a certain day ...
If you want a view of all the past searches this should get you want you want.
Download a copy of your past searches
Visit your Web & App Activity page.
In the top right corner of the
page, touch Menu More> Download searches.
Choose Create Archive.
When the download is complete, you’ll get an email confirmation with
a link to the data.
From the ...
I suspect 1444936291238326 should be parsed: 1444936291 and 238326 with the former the Unix timestamp for not just time of day but day too: October 15, 2015 @ 7:11pm (UTC).
At this time of year most of Indiana is GMT-5, so 7:11pm UTC not far off 3:11pm local there.
238326 might be for seconds.
There is currently no way to do this. However, using search history to keep track of what websites you visit is like installing CCTV in your bedroom to keep track of your socks. Your browser is likely equipped with a history function and cloud sync to make sure you don't lose it.