Brian, your wife can still apply ILR even after June as long as long as her visa is still valid. 28 days before her 24th month stay is just the earliest date she can apply. Don't be confused with it. If her English test is on June and the test result will be released in July for example, then you can apply ILR if she gets the B1 grade.
Biometrics form is included in the FLR and ILR forms. UKVI will send her a letter for biometrics after you sent the application. This can be done in the post office that has the biometrics machine. You need to check which post office near you that has that.
In post #18, I gave you the link for the form. Just click it. Form FLR(M) and the guidance note. It's just at the top of the page.