In the Define Filter window, at the bottom, there are some additional Options. The default is that All rules must apply. Rule1 AND Rule2 AND Rule3. There is an option At Least one rule must apply. Rule1 OR Rule2 OR Rule3.
So for your example set a rule to look for “England” and a rule looking for “Ireland” with the At least one rule must apply. “England” OR “Ireland”
To look for a blank/empty field needs to use a Regular Expression. In the Filter rule for the field in question enter a period (.) in the field to match for any character and check the box at the bottom of the filter rule option Use regular expressions. With this rule you are searching for any entry in the field. Back in the Define Filter window, there is an additional option to Return values that do not match the filter rules. NOT the records that would return true for the rules above.
And remember, you can nest filters that you create. Depending on the desired filter rule areas, there will be rules to reference other filters already created. So you can have the filter rule selecting “England” or “Ireland” being referenced by another Filter you create even from another area of the database… It is a process of figuring out all of the parts of an ultimate filter and which components can be combined.
Ultimately, you run the final filter you create and Gramps will process the sub-filters to hopefully find what you are looking for.