1)A deletion anomaly is defined as the unintended loss of data which happens due to deletion of other data on which primary key is not dependant
An insertion anomaly is defined as the inability to add data which is usually done to the database and this happenes usually in absence of other data.
Modification anomalies to change the data without any notice
They are considered bad because they lead to irregular results when queries are made and the exact data is not shown.Example deletion anomaly deletes the data without notifying the user and it leads to wrong results when query is made.They can be solved by normalization which leads to right results.
2)A closure is defined as a set possible Functional dependencies (FDs) which can be derived easily from a given set of functional dependencies Now If we have F which is used to donate the set of FD'S which happens for relation denoted R, then a closure of a set of FD which is implied by F is denoted by F+