Google Finance – Integrate with Google Sheets for Real-Time Data

Your attempted set of formulas cannot work as intended. You have the ImportHTML function in cell B1, a list of dates in column A and commands such as

=IF(TODAY()=A6,$B1) 

in column B. An issue with this formula is that the condition will become FALSE after the day passes, so the data will be lost. And trying to rectify with =IF(TODAY()>=A6,$B1) would not help, since then the data will keep on changing.

The basic limitation here is that a formula cannot stop being a formula on its own. You want to "freeze" it in place, replacing with a static value. Apart from manual editing, this can only be done with a script. Here is a script that produces a record in the form similar to yours:

function addDateAndValue() {
  var url = ' url of your spreadsheet ';  // put url here
  var ss = SpreadsheetApp.openByUrl(url);
  var sh = ss.getSheetByName('Sheet1');   // or another name
  var height = sh.getDataRange().getHeight();
  sh.insertRowAfter(height);
  sh.getRange(height+1, 1).setValue(Utilities.formatDate(new Date(), "GMT", "mm/dd/yyyy"));
  sh.getRange(height+1, 2).setValue(sh.getRange("B1").getValue());
}

Namely, it adds a new row at the bottom of the current data range, puts today's date in column A and puts the value from B1 into column B. The copied value is just that, a number (or string), which is not going to change anymore.

You can make this script run daily by adding a trigger via (Resources > Current project's triggers).

As filter command documentation says,

In order to filter both rows and columns, use the return value of one FILTER function as range in another.

Like so:

=filter(filter(A4:L8, (A2:L2="Email")+(A2:L2="All")), A4:A8="Email")