It sounds like what you want is this:
insert into items(projectid,description)
select P.ProjectId, '@descriptionval'
from Projects P
where P.Active = 1 and P.ProjectID = '@projectidval'
If I understand your schema correctly, you can't do an INNER JOIN, because tableA doesn't have the matching row yet.
Now for the delete, you do have both row now, so you will do the join:
DELETE FROM Items I
inner join Projects P on I.ProjectId = P.ProjectId
where P.Active = 1 and I.ProjectID = @ProjId
UPDATED based on OP's comment to question and his own answer. This should allows a 1 to many releationship between Projects & Items.