For 1, the only two ways I can see both involve changes to the core Fabrik code.
1) Modify where we set up those dropdown menus. The problem there is that we can't just change the existing "EQUALS" default, as that would mess up everyone else. So the only "proper" way of doing it would be for us to add this as YAFO (Yet Another Option) on the list settings, which frankly isn't going to happen unless someone pays us to do it as a custom job (I'd guesstimate about $100).
So unless you want to do that, you'd have fork Fabrik on github, and tweak the main list model, ./components/com_fabrik/models/list.php, around lines 6316 and 6547, where we set up the 'statements' dropdowns, and set the last arg to be 'CONTAINS'.
Code:
$opts->statementList = JHTML::_('select.genericlist', $statements, 'fabrik___filter[list_' . $listRef . '][condition][]',
'class="inputbox input-small" size="1" ', 'value', 'text', 'CONTAINS');
... and ...
Code:
$jsSel = JHTML::_('select.genericlist', $statements, $prefix . 'condition][]', 'class="inputbox" size="1" ', 'value', 'text', 'CONTAINS');
... and run that code instead of our github, regularly merging the joomla3 branch in to your fork. But of course, that means you are pretty much on your own for support.
I tested those two little changes above, and they work, btw. I just can't put them in the code, as explained above, without make the default a "YAFO" in the list settings, which is an hour or so's work.
2) Use Javascript to tweak the default for the dropdown when the popup is first initialized, and then as each row is added. This would require us adding a couple of events to the advanced-search.js, during initialization and then in addRow(), which we could do as part of your sub, as it's just a couple of quick lines of code. Then you'd need to come up with some custom form_X.js, with event handlers, to change the selection when those events fire. Shouldn't be too hard, but you'd need some JS chops.
Let me know which approach you want to take.
As for your 2, of putting the advanced search directly on the page ... I've only had a quick look at the code, but that wouldn't be entirely trivial. There's a lot of assumptions in the code about it being in a popup window.
-- hugh