My freezer is filled with ice - is it safe to to use it as is?

If you have a newer freezer that is "frost free" as Wayfaring Stranger mentioned you should get your freezer repaired or replaced. From personal experience this can happen over time even with a frost free freezer, the important part is that it's the right temperature.

As far as safety, the FDA states pretty clearly that freezers must be at or below 0F. You can get a thermometer pretty cheaply to test this out. I would do this immediately and before storing any food in your freezer.

As far as methods to defrost food, there are plenty of other posts on that on this site.

In regards of food safety the ice layer should not do any harm. But be aware that the ice layer is working as an insulater and thus increases the amount of electricity consumed by the freezer. So it´s advisable to remove it from time to time for this reason alone. For details see: here and here.