Just thought I would let you know were I am at. I replaced the code with your last package you sent me. I did not attempt a new install as the field you found missing on the database did get me a bit further. So what I did do is generate some test data via the piwik plugin and most of the records were created, however, there was a couple of repetitive errors for some record types.
It is an early stage and I don't completely understand the records being inserted at the raw level, so fyi:-

--> turn not null off for URL field of PIWIK_LOG_CONVERSION as null was being set from an empty param for on the insert statement. I checked the MySQL and it does have not null on but allows an empty field (none). In php I have avoided using the "?" params method so I am not an expert :-) but I do recall with firebird using an empty string param does result in a null being use. Turning off the not null did resolve this error.

--> the next error was:- PHP Warning: fbird_query(): Dynamic SQL Error SQL error code = -303 conversion error from string "" in E:\Apache2.2\htdocs\piwik\core\Tracker\Db\Firebird.php on line 229
Seems to be caused by a very large number (e.g. 3991561144) being inserted into the BUSTER field of type INTEGER. I don't fully understand this field but it seems to be a unique identifier which is indexed. Only occasionally is the number this large so I don't know if it justifies being altered to BIGINT. MySQL has it as int(10).

--> the last generator error is PHP Warning: fbird_query(): Dynamic SQL Error SQL error code = -104 Token unknown - line 4, column 48 , in E:\Apache2.2\htdocs\piwik\core\Tracker\Db\Firebird.php on line 229 which is caused by a multi insert stmt of the form:
INSERT INTO piwik_log_conversion_item (idaction_sku, idaction_name, idaction_category, idaction_category2, idaction_category3, idaction_category4, idaction_category5, price, quantity, deleted,
idorder, idsite, idvisitor, server_time, idvisit)
VALUES ( ?,?,?,?,?,?,?,?,?,?,?,?,?,?,? ) , ( ?,?,?,?,?,?,?,?,?,?,?,?,?,?,? )
which, I believe, is not supported by firebird.

That's what I have on the generation. But, like I said, I am at an early stage so don't worry about these until I investigate further.

On setting up email report I get a SQL syntax error on the save step. I have yet to trap the SQL stmt to find its cause but it should not take too long. Have you set up any email reports? If so did you get an error?

Occasionally, when I return to the Dashboard page some widget, which did display ok, now returns:-
Date format must be: YYYY-MM-DD, or 'today' or 'yesterday' or any keyword supported by the strtotime function (see http://php.net/strtotime for more information)

example
Backtrace:

#0 E:\Apache2.2\htdocs\piwik\core\ViewDataTable.php(1206): Piwik_Date::factory('previous30')
#1 E:\Apache2.2\htdocs\piwik\core\ViewDataTable\GenerateGraphHTML.php(133): Piwik_ViewDataTable->hasReportBeenPurged()
#2 E:\Apache2.2\htdocs\piwik\core\ViewDataTable\GenerateGraphHTML.php(97): Piwik_ViewDataTable_GenerateGraphHTML->buildView()
#3 E:\Apache2.2\htdocs\piwik\core\Controller.php(241): Piwik_ViewDataTable_GenerateGraphHTML->main()
#4 E:\Apache2.2\htdocs\piwik\plugins\VisitsSummary\Controller.php(78): Piwik_Controller->getLastUnitGraphAcrossPlugins('VisitsSummary', 'getEvolutionGra...', Array, Array, 'This is an over...')
#5 [internal function]: Piwik_VisitsSummary_Controller->getEvolutionGraph()
#6 E:\Apache2.2\htdocs\piwik\core\FrontController.php(138): call_user_func_array(Array, Array)
#7 E:\Apache2.2\htdocs\piwik\index.php(53): Piwik_FrontController->dispatch()
#8 {main}

Again, I'll have to set some traps as it looks as if the global date setting is becoming corrupted.

Looking at the config there is some kind of debug log that I need to understand as it will save me a lot of time patching the php code to find errors (of any).

I keep you informed if I find anything tangible.
Have a good weekend
David